transferring the kubuntu ssd from a dead dell to a live dell of the same model and configuration

Hi all,
I'm new to Kubuntu but it's going fine. Although this question concerns Kubuntu, the answer will probably be true for all distributions.

I have a dell 780 optiplex, the psu has failed.

another working machine is much cheaper than buying another psu.

the new machine will be fitted with the HDs and the SIMMs and, of course, the ssd containing my installed Kubuntu complete with all my valuable data!

am I being foolish in believing that this will just work seamlessly?

regards

Chris