Will a Wings of Liberty campaign be any different with the Heart of the Swarm extension?

you have the new UI features (workers per mineral patch, change on the look of attack commands, etc.) since they got implemented in WoL too. However, I have not noticed any changes in the units as all the Terran units are Campaign only (marauder don't have stim, medics, banshees with splash, etc.)

A short answer to your question: Your WOL will not be affected by HOTS in anyway!

(The only changes if you will, is the patch released prior to the release of HOTS - this is not due to HOTS as it was a patch for WOL)

There is no difference at all, whether you play with, or without HOTS expansion.