Really depends yes, but I wouldn't say its undoable at all.

I worked in CS for a year and when I was up, I was extra cheery and bright. The epitome of sunny disposition. *vomit face* lmao
Clients loved talking to me on the phone, my smiley voice made me sound willing to help and I got excellent reviews. Even the grumpy ones find it hard to yell at a chirpy person offering to go the extra mile for them.

I was way more productive too and helped a lot more clients than usual due to my mutli-tasking super powers that kick in during such times.

On the flip side, when depro, I'd fake the nice helpful voice until it was over, then go smoke a lot of cigarettes and cry into my pillow.

I doubt your bp will interfere especially given the fact that you work half day AND you're in a safe environment. Its a sweeet deal getting to work from home and for so few hours. That's a bp friendly job if ever there was one (in my book anyway) and its something, I'm working toward right now, although I would personally prefer more hours.