From Lion I'll Downgrade to Snow but Will I Be Able to Install XCode 4.1.1?

Hi. I'm running on safe mode in my iMac now (iMac Late 2009 i7) which I have to take to the shop because it may have a damaged GPU and it may have been caused by upgrading to Lion (the iMac is just one and half years old and is only put to sleep. Before it crashed, Safari would become garbled under Lion 10.7 or 10.7.1 every so often when I scroll. Maybe I shouldn't have bought Lion so fast but Lion has its advantages).

I will need to buy my friend's MacBook Core Duo which is quite inexpensive (it's not the one with the 4MB cache, 3GB, standard hardrive, battery life says normal, 2007 model with Superdrive, iSight and wifi) to continue some work there. In my Time Machine backup, there is an XCode 4.1.1 installer there (which is good and smart of Apple to do that for cases like this). I will save that but will it install on the MacBook with Snow Leopard? Or should I save the Developer folder instead of the Install Xcode app (the installer) that was downloaded from App Store under Lion?

Any recommendations are welcome.

Thank you in advance.

Gbu.