As the title says, is a Turbo 8088 (or NEC V20) fast enough to make the Mode 13h chunky 320x200 usable, or is VGA just not a good match?
It's a simple question of bandwidth: It depends on how many pixels you're going to be updating at a time. Your memory bandwidth to a VGA card on an 8MHz NEC V20 is going to be somewhere between 240KB/s and 360KB/s. If we assume the best, that would equate to about (360/64=) 5.6 frames per second if you're updating the entire screen every game tick. However, game rendering isn't free, so you should roughly divide that in half, so it would be reasonable to expect a framerate of about 3fps if you're updating the entire screen every frame.
So the trick is not to update the entire screen every frame
There are some games that only update portions of a frame, such as graphical adventures where you move a small character around a static screen, and those would be just fine. Or, if you had to update a large portion, maybe settle for half the screen, like a driving viewport on top and the dash/steering wheel on the bottom.
One of the most well-optimized games I know of to showcase systems is Indianapolis 500. Download that, and run it on your system and watch the (impressive) demo that plays when you hit a key at the title screen. Note how it looks visually. Then, rerun it with "indy /c" to force CGA mode, and then watch the demo, and you'll notice it's faster because it has to update 1/4th of the memory that it would have to update with mode 13h.
Maybe if you mentioned what kind of game you were thinking of, we could offer more targeted advice and techniques.