Mmmm... not a very good idea. I can think of a couple reasons why this in an inherently bad idea.
1. A ten run deficit doesn't mean all that much.
In the overall scope of the game, you're going to lose 99% of these games. But these very same Seattle Mariners got their asses whooped by the Cleveland Indians after being up 14-2 in the sixth inning. The Indians have come back from deficits of 9 or more runs three times in the last two seasons. In two of those contests, they won the game by 8 or more runs.
Putting a position player on the mound assures you of two things: (1) you've given up hope of winning the game, and (2) you've lost the ability to use the player later in the game.
2. Non-pitchers are at greater risk of injury when pitching.
Non-pitchers don't pitch for a simple reason... they aren't good at it (or at least are good enough at hitting to warrant a positional spot). The day-to-day workouts that pitchers go through are vastly different from positional player workouts, all the way down to warm-up stretching. Additionally, position players do not consult with the pitching coach on a regular basis, so their pitching mechanics are often not too good.
When you have a player that isn't used to pitching, and doesn't have the proper mechanics to pitch, you're inviting trouble. For one, it's a lot easier to pull a groin or sprain an ankle during the stride towards home plate. Poor mechanics also lead to shoulder and elbow problems, that, yes, can manifest themselves after only one trip to the mound. Jose Canseco missed half a season with the Texas Rangers after straining an elbow trying to throw curveballs in relief.
On top of that, consider that the batters faced by the positional player all have a considerable advantage facing a non-pitcher, so the likelihood of getting struck with a batted ball increases. It's only sixty feet, six inches from home plate to the mound, and 'muzzle velocities' from batted balls are often more than 120 MPH.
3. Daily transactions make it easy to avoid overpitching players.
In general, professional baseball teams carry between ten and twelve pitchers. With a five-man rotation, this leaves five to seven relievers, one of whom is a 'closer'. Five relievers should be more than enough to pitch nine innings. If you've run out of pitchers in a nine inning game (especially in the American League where you don't have to pinch-hit for them), you are a poor manager.
The worry is that a pitcher will be overworked, and he'll be tired and won't be available to pitch for a few days. While that may be true (although a tired arm is an indication that you don't throw the ball enough, not that you throw the ball too much), the way transactions work give clubs a typically endless supply of pitching.
Because of the near complete lack of restriction on minor league transactions, a pitcher can be purchased on a single day's notice to pitch in the majors the next day, and then assigned right back to the minors after the game. More drastically, a club can also place anyone they want on the 15-day disabled list, and call up a spare pitcher for more prolonged duty.
Now, Jose Oquendo is a different matter. The same options apply for finding new pitchers, but a manager should not manage the team as though a game is going into extra innings. Add in the fact that the Cardinals play in the National League, and Whitey Herzog (who's a notorious substitutional manager) probably used up all of his pitchers AND bench players in pinch-hit situations. I'm guessing Oquendo was probably the last player left on the bench, and was told that he was finishing the game regardless of the outcome. In that case, you just shit in your pants and keep swimming.
Perhaps I should clarify some things...
As mentioned above, five pitchers isn't enough for a nine inning game. This is true, but it's due to some unfortunate circumstances brought upon by Tony LaRussa and general stupidity.
38 pitchers in major league baseball have recorded 300 or more complete games. Of these 38, only one, Gaylord Perry, pitched after 1979. The leader among active pitchers for complete games? Roger Clemens with 116 (as of this writing). No other active pitcher has 100 (although Greg Maddux is at 99 as of this writing). Starters don't pitch as many games anymore, and they don't finish the ones that they pitch in. But what about relievers?
When Rollie Fingers and Goose Gossage were dominating their era as relievers, they were averaging 117.9 and 118.4 innings per season, respectively. By the time the eighties rolled around, closers like Dave Righetti and Dan Quisenberry were averaging just over an inning per appearance. When Tony Larussa took his juggernaut Oakland A's to three straight World Series with Rick Honeycutt as the setup man and Dennis Eckersley as the closer, it cemented the role of the closer to one inning, and the necessity of a one-inning setup man in the minds of most baseball folks.
Over that span of 25 years, the traditional four-man rotation gave way to five-man rotation. At about the same time, pitchers began seeing drastically reduced innings totals, not just season totals, but innings per game averages.
The reason is because you need to throw to gain and maintain arm strength. The majority of sore arms are a result of NOT throwing enough, not because of throwing too much. Unfortunately, by the time you reach the big leagues it's too late, because you've been pitching in a five man rotation for a number of years, and even prior to that you were probably on pitch counts in high school, and were too busy with other stuff to throw on the side. Weights don't help build pitching arms like they do batting swings. You've got to throw.
There's no reason why starters shouldn't be averaging six or seven innings per start, and relying on two pitchers at most to finish off games.