Your Corvette's frame is more than a simple skeleton on which you hang the fiberglass body and the various suspension parts. Your Corvette's frame is an absolutely critical component for handling and safety. If your Vette's frame is bent, then by definition it has been weakened, and could pose a danger to you in addition to making your car impossible to align correctly.
The tricky problem is that frame damage is a lot harder to identify than body damage. In most cases, the frame is concealed when you're considering making a purchase. The seller may not even know about old frame damage, and it's also possible that the frame may have been repaired incorrectly. This becomes more true as cars get older, as there's been more time to accumulate damage, reporting fundamental damage (through branded titles and CARFAX) used to be much more sketchy than it is now (and even now it's not that reliable), and chassis designs were weaker back in the classic era.
But the good news is that Corvette frames are simple - or at least, the old ones are. C5 and C6 Corvette frames are fully state-of-the-art hydroformed space frame designs, and a well-equipped modern body shop will have all the specifications and tools to evaluate these cars. But for the older machines, a good body shop can check the frame using simple tools and basic measurements. An experienced frame technician can detect bends, twists, warps, and general misalignment in your C1 through C4 Corvette frame, and repair these faults with relative ease.
Probably the most common crash-related frame damage for old Corvettes is sway. That happens when the front or rear of the vehicle is hit with a side blow. If there has been a side impact at the front bumper, it can sway the front frame rails over. In older vehicles, there was a lot of forgiveness and adjustability built in. So shops could adjust a little bit of side sway out when they fixed the fiberglass and when they readjusted the suspension, but the car will almost always pull to one side thereafter, or have other peculiarities in driving.
Another damage condition is diamonding. That's when one frame rail is moved forward or back in relation to the other. For example, if you hit something head on at one side of the car, such as running into a phone pole, it will move the damaged frame rail rearward in relation to the other frame rail. This amounts to a double-sway situation, with sway in one direction at the front end, and in the opposite direction in the rear. If you've seen cars "crabbing" down the road, where the car actually sits at an angle to its direction of straight travel, that's what you're seeing.
Rust is not generally such a big deal for Corvettes, but if your Corvette frame has suffered rust damage, you need to have that carefully evaluated. I'm not talking about the surface rust that all frames will accumulate, but rather the kind of "flaking off in big chunks and leaving holes in the metal" kind of rust that we see throughout the Midwest and Northeast United States, where the roads are salted in the winter.
If the rust in your frame is localized, you can have the rusty portion cut out and replaced with a new piece. This is always custom work, because Corvette frame rails are not perfect rectangles - they have a tapered shape, with specific bends. So this is a job for a professional fabricator who can exactly match the original shape and then grind the welds smooth again. Many Corvette restorers will go even further - refusing to use a rust-damaged frame and instead opting for a complete replacement.
TIP: One thing that is true - if there's significant frame damage, you're usually looking at taking the body off the car. Use this as an opportunity to restore the body/frame pads, bolts, and cups. They're inexpensive and easy to replace when you have the body off the car.
Finally, when your frame comes back from the body and fab shop all clean, straight, strong, and true, you'll want to paint it as soon as possible to prevent rust from forming. For the purest restoration, paint it in the same color and with the same materials used by the Chevy factory. That is usually just black paint. To hide light rust pitting, signs of welding, and other repairs, some restorers will have a frame powder-coated, and then painted with the original color as a top coat. This provides maximum long-term protection and a great finish. If you're not going for a full-on restoration, just have the frame powder coated for maximum durability.