"An economical person" (and similar phrases) seems to be a fairly common example given in dictionaries, so I think the answer is yes. Personally, I wouldn't tend to use it to describe a person, except, perhaps, with a subject complement, such as "economical with her money" or "with the truth". This may just be my personal preference, though. Plenty of other people seem happy with it.
Now that matching mole has mentioned it, the more I think about being "an economical person", the more silly it sounds. How can a person be economical with their Self? Perhaps they shave off their hair so they save time and energy cutting it themself, never mind paying to get it cut.
I think that in fact we often say of someone that they are " an economical person", meaning they are careful how they spend their money.