You won't know for sure until you contact a lender and see what the current guidelines are. Other things the lender will want to ask the HOA is what is the ratio to owner occupied units vs. non-owner occupied, 48-49% is normally the cut off, exceptions are possible if at 50%. So, this one person owning 4 units may not be your only issue.
For a quick response, send an email to Danny Baldwin at Pacific One Lending at DBaldwin@Pacific1Lending.com put in the subject line: "ques. re: a condo for Emily Knell"
Even with the owner vs. non-owner occupant issue, when you go to sell, if the ration is say, at 35% today, it could be higher in the future. It can hurt your future value if the condo community becomes a "cash buyers only neighb" in the future.