Yes, it can be.
https://www.mayoclinic.org/drugs-supplements/valacyclovir-oral-route/side-effects/drg-20066635?p=1
"Incidence not known
...
hair loss or thinning of the hair"
That means it happens, but they don't really study it to find out how often.
Is it happening to you, or are you concerned about it? If you're concerned about it, know that it doesn't happen to everyone. If you already have alopecia, it may be a bigger concern, but talk to your doctor.
I definitely have this side effect. I started to remember when I took shower s clumps of hair was coming out of my head. Which also rendering that that's around the time I started suppressive therapy. Now I have no nape hair. Thinning crown and no edges