Would the inhalation of paint or other chemicals cause complications
for someone who suffers nosebleeds due to Osler-Weber-Rendu Syndrome?

I'm not a doctor, I just play one on google answers.

IMO, The answer to your question is an emphatic yes, but it largely
depends on the chemicals.  Not all paints will cause problems. 
Wearing a respirator will reduce greatly most problems.  Many choices
are available to limit exposure to most volatile chemicals.