Nope.
More players that would have quit or gone pro are sticking with football for longer because they are getting paid to do so. Every player that sticks around an extra season reduces the need for one freshman recruit.
The old transfer rules really reduced the value of transfers to their new school, and increased the cost of transferring to the player. On top of that, a player could only transfer once.
Even the inter-school movement within the P4 is not a zero sum game. Player talent balances out quickly between teams at this level. In the old days, if a team was 5 deep at cornerback in a class, the coach would run off one or two of the players around junior year, and the extra player would have a hard time finding a new team. Now, each roster reallocates every season, and less effective players simply drop to a lesser program, rather than getting run out of the sport.
Furthermore, now, a 21 year old MAC starter or top reserve is much more valuable to a major conference team than a 3* and even many 4* frosh. Why bother gambling on a frosh that won’t stay if they are good when you can use that spot on an older sure thing? In addition, FCS upgrades also provide a source of older talent, so even the lower level schools are incentivized to grab transfers rather than a marginal freshman.
This phenomenon is more dramatic in basketball.