The answer is yes. Those types of viruses that insert their genomic material into the host cell genome can cause mutation. In fact, this is originally how the genes that cause cancer (oncogenes) were discovered.
As far as the feasibility of "giant mutated undead spider guys" (GMUSGs)... no. The mutation is on a per-cell-infected basis and the descendants of that cell line.
The main problem with viral mutation vis-a-vis GMUSGs is that the virus is mostly messing up host processes, such as contact inhibition or genome proofreading, that prevent transformation into cancerous cells.
Zombies make more sense, as you could cause neural tissue damage that results in insanity and aggression. Transferring the virus via bite would be trivial
If you (or anyone) would like to ask a question about a viral mutation causing a specific outcome, I'm sure I could dig through my journals and find something. Kinda had to paint with broad strokes here.
TL;DR: Viruses mutate things in a way that messes them up, not in a coordinated way that could result in new, functional structures.