No, a 3.5 isn't going to improve to 4.5 by using a heavier racket but a 3.5 that is working hard to move up to 4.0 and 4.5 over the next 2 to 3 years should probably play a racket that can handle that level. the player's skill level trumps gear tweaks but it is wise to play with gear that is a good fit for your current level and target level. I too have seen excellent players win with crap rackets. I have a friend who played D1, was an alternate on a world team tennis pro team and is in his college's tennis hall of fame. He played an oversized light Wilson piece of crap probably because he got it on sale and he beat almost everyone he played even in local mid-level leagues though he rarely practiced and had significant knee issues. But, he if was trying to win tournaments at his level (4.5 or 5.0), I think he would be more competitive with a better frame for his level.
No disagreements. If you saw what I posted, I'm just questioning the logic that rec adults who are taking up the sport casually need to play with heavy racquets aka real racquets. As I said, unless you are consistently going to play high level 4.5s or above, which most rec players in their lives will never do, there's no real reason to move to a heavy racquet, and in fact lighter might be better. In the end, try both and go for what you like. OTOH if you're serious about tennis and are committed both on court/off court to move up, then yes, you'll need to seriously think about transitioning to heavier frames.