Close, but not quite.
There is a benefit that if a veteran (might have to be vested vet) gets signed to the league minimum for his years of service, his cap hit is only that of a 1st year player.
Easy, made up, round numbers:
If you sign a 7 year vet, let's say the minimum for him is $1MM per year. An UDFA rookie is $500k. You sign him to $1MM for 1 year (and even can give him a paltry signing bonus...it was $70k last I checked) and he only counts for $500k against the cap.
The intent is obvious: Make it so vet fringe players don't get put out to pasture too early. And coaches don't pull their hair out when the 22 year old kids can't play punt coverage.
In OBJ's case, I don't know how this would apply due to his offset contract. I suspect it would not. Assuming we signed him, he'd get 1/17th (or 18th, I forget how the bye factors in) of the vet minimum for each game he's on our roster.