<p>I was wondering if adding (an) extra fan(s) (not connected to the printer, but blowing on the print area) could improve the quality of PLA based prints(printing at 210 C). The printer already has a built in fan with a fan shroud that directs air to the hotend, but is it beneficial to add an extra fan in order to get better results on overhangs, fine details, etc, or does extra cooling negatively/not affect print quality? </p>

The printer already has a built in fan with a fan shroud that directs air to the hotend
Unless your printer is defective, it may look like so, but the airflow should really be directed towards the print, not the hot-end
.  Cooling the hot-end will at best just waste energy, requiring extra heat to keep it hot, at worst affect your print quality negatively.
is it beneficial to add an extra fan in order to get better results on overhangs?
The issue with external fans, not connected to the printer, is that you can't properly direct their ariflow, so:
you
will
direct some of it on the hot-end itself (see above on why that's not good)
you will potentially cool your print unevenly, which - depending from how much, how fast, and what type of filament you are using - may warp your prints
That said, depending from a number of factors, including your ability to position the fans appropriately,
you
may
gain some benefit from them (I saw people doing this to help with PETG stringing), but I would recommend instead to upgrade the part fan of your printer (e.g.: larger diameter, higher RPM) and your duct (better focus on the extruded filament)
, as these upgrades will have no drawbacks and will perform consistently on each part of the print.
For most common printer, there are printable mods that allow to do both, often available off thingiverse or on dedicated user community forums.