Black plastic piece on top = UIM = upper intake manifold
Aluminum piece the UIM is bolted to = LIM = lower intake manifold...which is bolted to the cylinder heads
Throttle body (bolted to driver's side of UIM) = TB
Any coolant leak that is puddling coolant onto the topend is due to either a bad gasket or a cracked/burned/warped plastic UIM--and thus could easily become internal. So yes, unless you get this fixed your engine is in mortal peril. Furthermore, EVERY 3800 produced prior to about 2005 WILL develop one or more of the dreaded coolant leaks...they are built-in design flaws courtesy of GM bean counters.
Now you gotta help us to help you...is there coolant puddling on the LIM? (In the area and recesses around where the fuel injectors are?) Is it mostly toward the TB end? If that is so, it is probably, as BillBoost37 suggested, a UIM-to-TB gasket.
Is the coolant puddling all over the LIM? If so, that may also be UIM-to-TB gasket, or UIM-to-LIM gasket, or a crack/burn in the UIM--but in this case, the leak is already internal and coolant is likely puddling inside the LIM and leaking out under the UIM-to-LIM gasket.
First thing I would do, were I you, is to remove the TB (10mm socket), inspect the UIM-to-TB gasket, and also look into the "throat" of the UIM with a flashlight to see if there is coolant wetting or puddling inside the LIM. Then report back
