I think for a felon to attempt to purchase is a crime, in itself, even if they fill out the form accurately.
Meanwhile, we've discussed this in a couple other threads, and while the stopped transactions typically number over 70,000 in a year, prosecutions typically stay under 100, and convictions under 10.
This leads one to wonder about the percentage of stopped transactions that are due to old, dropped cases, and how many are just flat-out unwarranted.
Frankly, I don't think an NICS check stop at a dealer is going to keep a determined crook or sociopath from finding a weapon via alternate means. And, I think the existing laws (for instance, ten years federal prison for straw purchasers, in theory) would have plenty of teeth to accomplish the desired ends, if they were prosecuted in good faith.