I never said you wouldn't notice a difference of some sort no matter what you ride with them.
However, he is scrimping and saving to do so. On the street, RT forks are 100% overkill. You can talk about going in too hot, margin of safety, etc and I'll just say to use the money on more trackdays or a school to learn how to ride. That will give you more margin of safety than any equipment can.
On the track you use the suspension more than that street therefore you will notice it more and faster. But again, once you spring it for your weight, the stock stuff will work and you can go very fast on it. There are guys well into A group on stock stuff
It comes down to the skrimping and saving...if you have the money to blow by all means get them. If you don't, trackdays/school will be far more benificial to your ability and speed than any piece of equipment you can buy.
I've been riding over two decades and started going to the track in 2000. RT's are never overkill IMHO. They soak up the bumps so much better than anything I've used. Do you need them, no. But then again you don't need a motorcycle either, most don't. Suspension needs to be sorted for your weight but you won't get the feel out of the stock forks that you can with the RT's, CARTS, etc.
Unless you are perfect you'll cook a corner once in a while whether that is in the twisties or on the track. I've taken a routine corner that I've taken hundreds of times before, only there is debris or something else in the road, and modified or aftermarket forks helped. Not only with feel, but soaking up my shot corner than I'm now trying to ride out of. Anything that increases feel and soaks up the bumps better means faster times at the track but also means a nice safety margin on the street. Overkill for safety isn't a waste of money to me but may be to you, YMMV. Aftermarket stuff and bump absorption will also help with fatigue at a track day. I don't know about you but by the end of the day I'm fatigued, especially in the TX heat. I noticed a difference going to track days back to back with OEM forks with spring changes and Ohlins gear. By the last session with Ohlins I was less fatigued, and had more in human tank for the last session of the day, which many times I'd skip as in my time I'd seen more wrecks late in the day than any. (that and the first session after the winter with a few riding too hard too early).
You said street "No way" and I'm saying bullshit to that, nothing more. Dialed in aftermarket suspension has saved my noodle more than once and enabled me to be low/highside free for over a decade street and track.
Overkill on the street is awesome in my view, Greater safety margin.
And OP, I don't know anyone who has gone Ohlins who has said they wished they hadn't. RT's are expensive (I've bought both sets of mine used) but the carts are a much better buy. If you want to scrimp (I have on most of my parts) then be patient and routinely checked the classifieds here. I've seen many sets of RT's as well as Carts and TTX's go up in the classifieds for substantial savings over new in the classifieds here. This is how I gathered at least half of my parts, by being patient and waiting for those with bigger wallets than me, sell their swag.