Depends on the game. I know less than zero about bridge, so I would be doing a disservice by agreeing to play even with mediocre players. Otherwise, if it’s something I at least know the basics, sure I’ll join.
If anyone asks you to join them in a game of Fizzbin, just say no.
When trekking in Nepal a group of us watched a fellow trekker join in with some porters who were playing some sort of card game. None of us ever really understood the rules of the game, especially the trekker, and the porters were playing for money. Needless to say, the trekker didn’t fare well, but it was a very small amount of money to a westerner, and everyone had a fantastic time shouting encouragement or various interpretations of rules, and passing the apple brandy. I came away fairly well convinced that it was a real life version of Fizzbin.
I tend to have non-standard victory conditions, which is a fancy way of saying that I play games to have fun, not necessarily to “win” by the rules of the game. Depending on circumstances and who I’m playing with, my victory conditions may include prolonging the game, achieving a specific non-“win” outcome, confusing other players, or even annoying a specific player (only to tease them, though, not in a mean-spirited way). In essence, when I acknowledge going in that I’m not good at a game, I aim to be the world’s worst swordsman, rather than the second best.
Playing as a rank amateur against expert players offers a great deal of scope for my approach to play, because it affords opportunities to be disruptive to their practiced strategies. Every time I see a “WTF is he doing?” look cross one of their faces, I tally a point on my internal scorecard. 
Note that I refrain from this in partner games, unless my partner understands and is agreeable to this approach. If the game in the thread hypothetical is a partner game, I’d at least insist on switching partners periodically, so none of the expert players gets stuck with my shenanigans the whole time.
Thread relocated to the Game Room.
Go, like golf, allows handicaps to cancel skill advantage. With 5-stone handicap or so I might hold my own against amateur shodans. Similarly, I’d have a chance at backgammon if I started with the cube, or with opening doubles. Once upon a time I was near-expert at contract bridge, but by now I’ve rusted worse than the Tin Woodman at that game.
Not to disagree with your post, but I can’t resist pointing out that of course, once the skill gap gets sufficiently wide in chess (e.g. me, a fourth-team club player, vs an IM), the starting position is a “completely lost position” :).
To answer the OP, I agree with the majority here that I’d join in on the basis of making my (lack of) skill absolutely clear to the participants, so they have the opportunity to change their mind before I sit down. And if it still turned out to be an uncomfortable experience, I’d make my excuses and leave.
On the rare occasions where I am the expert, I’m quite happy to play other players of any level, and can usually find a way to make the game a good contest and/or a good learning experience for the other player. But then, I enjoy teaching.
Be flattered, remind them you’re still a noob, and join in. You’ll only ever be as good as the people you play with so it’s a great opportunity to improve your game. In the Army the game was spades. Most folks I played with were supercool about taking the novice as a partner. I personally liked the challenge of having the novice on my side partly because it made me play smarter, and partly because inexperience sometimes led to very aggressive plays that paid off big.
And then there’s the perks of a broader social circle that included the cooks and mechanics. Good friends to have when you’re spending a month on a field exercise.
I’m a slightly above-average Scrabble player and I’d play against a Scrabble expert. I’d get my ass kicked but I’d probably learn some fun new words.