Can I use an android phone running Ice Cream Sandwich to test apps created in Gingerbread? We will develop applications for android 2.3.4 (gingerbread) and because the emulator of my laptop is very unusable and the android x86 is not supported in my laptop, i'm planning to invest an android device to test the applications that we are going to create.

Since android ICS is the recent version of android OS, i plan to buy a phone running it. 

Would their be any compatibility issue i might encounter during my development? Or i could survive using that phone smoothly till the end?
In short, yes. Android apps are upward compatible as @ce4 said. But if you are going to build an app, its best to compile it on the latest version of android, ie Jelly Bean 4.2.1. This question would have been better suited on StackOverflow.