(In the US) Last I knew, no. That is, having the card and using it is as "credit" is not reflected in your credit report as a listing they keep track of.
Debit cards with Visa/MC logos do not equal them being actual credit cards because you are not "borrowing" money, even when you use the credit option. However, if you use the "credit" option, what it does (my understanding) is it can take a few days before being reflected on/to your bank account ... whereas "debit" is immediate removal. (edit: eg, it's kinda like writing a check)
Basically, if you are using an "online" method of using the debit card (have to slide it thru the reader/put in your PIN), there's not really any reason that I'm aware of to use it as a "credit" - eg don't push that button on the pad, just stick to the debit option. For one thing, many cards may have a dollar limit of how much you can use the "credit" option for as a method of reducing overdrawn-issues from the delay (vs. only being limited to total funds in your account via debit/online-PoS method).
If you're in a place that will take the debit card but does not have a reader/machine that accepts/deals with the PIN, then you may want to use the credit option (signature) instead.
Obviously, if you use the credit option and then have not enough funds in your bank account when the "charge" is posted to your account, that would likely be considered check-fraud or something, and could thus be reflected on your credit score (edit: if not resolved etc). But the use of it alone will not show up.
Lastly, using a debit card can apparently encourage some places (like rental car companies) to run a credit check, because they're a little more paranoid about them vs. true credit cards, which
can affect your credit score if it happens too often in a short period of time.