No. But it won't improve it much, either. The converter boxes put out good quality analog signals. You may see an improvement in less noise and fewer ghosts, but in the end, it's the old analog TV we've been watching for years.
I've done some side by side comparisons between our analog signal off the air and a converter box. Nobody that I've shown it to has been able to tell the difference . . .
EDIT for TECH-MAN:
These are at demonstrations at speaking engagements the NAB sends me to educate the public on the digital transition and station promotional events. We are using a two bay bow tie set top antenna on a standard analog set at distances up to 30 miles from the transmitter. The opinions are from the public at these events. Granted, we do work to get the best off air signal (many people at home don't), and we are comparing a Full Power Digital Plant (many aren't) to a Full Power Analog plant, but they are off the air comparisons.
For fringe reception at 60 miles, I would agree with you, but the vast majority of the population are not in fringe areas and there is nothing in this question to infer that this person is in a fringe area. We do population studies before we design transmitter plants to put the best signal over the target population so, playing the odds, they are not in the B grade contour.
I did concede in my original answer that there is less noise and ghosts, though . . .
The original question was does a STB > DEGRADE < the video. I think you and I are in agreement that the STB's output is on par with some of the best analog video out there.
BTW - Why don't I see you picking fault with other posters on this forum?