Is it possible to...

[dumbass]

Convert the bridge on my american strat, a "normal" two point tremolo bridge, to a telecaster-style bridge with pickup? (My guitar has swimming pool routing)

 

[3 Mile Stone]

My unexpert wild @ss guess is no. Maybe if it didn't have the swimming pool routing.

 

[Pietro]

You need a new guitar, not to mod the old one... That's just too much, and the beauty of a hard-tail tele bridge is wasted on a guitar that has all that wood routed out for the trem.

It can probably be done, but should it? No.