Pretty much any turbo timer and be installed to allow the alarm to arm while the car is on. All depends on how good the alarm installer is. And while inbuilt TT are good and convienent, most of them cant be changed from the basic 1 min cool down.
Yes, its good to take the last few km's easy before turning off your car, but giving it a few more mins extra cool down is always good. Hence why TT's are such a good things to have.
Not sure about your insurance company, but i have told mine what alarm i have and that i have a external TT and they said its fine, and insured me for it.