If it is a desktop (3.5") based drive with its own power supply, then definitely yes.
If it is a portable, USB powered drive, then very likely, but it will depend on what else you have the USB ports powering, and how voltage stable your PSU is.
The USB 2.0 standard is 500mA per port, so USB 2.0 hard drives are designed to run within those power limitations. Also note that a computer with 4 USB 2.0 ports should output a total current of 2A for all 4 ports combined. This is why some USB hard drives come with a Y-cable that connects to 2 USB ports. The extra plug gives an extra 500mA for drives can't quite meet the 500mA USB 2.0 power limitation.
The Pi3 can output a max of 1.2A for all 4 ports, which is less than the USB 2.0 standard. However, the Pi3 has no per-port limits, so it can output 1.2A from a single port and should be able to run a USB 3.0 HDD, as long as you aren't using other power hungry USB devices (if the total current draw from the USB ports exceeds 1.2A then something's gonna fail).
Another problem is voltage droop. Many 5V power supplies are designed for charging phone or tablet batteries, and batteries are not very sensitive to voltage fluctuations. As a result, many so called "5V" power supplies output much less than 5V under load (4.5V will charge a phone battery, but it won't ruin a Pi3).
Unfortunately there are too many variables involved to give you a definitive answer.
All that being said, I have used a variety of USB 2.0 and USB 3.0 portable hard drives on my Pi3 without any problems. Note, however, that my Pi3 is powered by a 5.3V/2.4A PSU with pretty good regulation. I have even successfully spun up 2 USB powered portable hard drives, but I could only access 1 at a time.
My mind is like a browser. 27 tabs are open, 9 aren't responding,
lots of pop-ups...and where is that annoying music coming from?