Will different CPU and RAM matter?

[Gary Clemans-Gibbon <garycg_(_at_)_angryrhino_(_dot_)_com>]

Hi All,

I have a co-located 3.4 web/mail box at a remote location with a P3 
1.2Ghz and
1Gb RAM (on-board LAN and video). At home I have another copy of the exact
same motherboard but with a Celeron 1.1Ghz and 512 Gb RAM.

The question is, can I install 3.7 on the box at home and then simply 
take out the HDD
and swap it into the co-lo server? Will it care that it was installed on 
a different CPU with less
RAM?

TIA.