If I recall correctly my 92 Beretta had a small hose going from the top of the thermostat housing to the reservoir. I assumed that it was to vent any air that accumulated in the housing, because it was the highest point of the cooling system. If this is the case you are correct in assuming that it is not needed; as long as the coolant system remains full.

By "water outlet", do you mean the outlet where the rad cap is?

Most bypasses - hoses and internally cast - are there to allow the coolant
to circulate while the thermostat is still closed.

This allows for a more uniform transfer of heat into the coolant, and a
more consistent temperature when the thermostat DOES open.

Usually the hose that comes out of the side of the thermostat housing is
called a 'Heater bypass hose'.  This is to allow coolant to bypass the
thermostat and go to the inside heater core from the engine core so you
start getting inside heat and a warm defrost before the engine totally
warms up so the thermostat opens.

It can sometimes take a 'long' time for the thermostat to open up here
in The Great White North.  We even block the radiator flow with
cardboard or a snap on cover to get more heat sooner.

Mike
86/00 CJ7 Laredo, 33x9.5 BFG Muds, 'glass nose to tail in '00
'New' frame in the works for '08

to provide coolant flow when the stat is closed

Bypass hoses perform 2 functions:

1) They allow coolant to circulate within the engine block BEFORE the
T-stat opens. If the T-stat were the sole flow path, then there would be
no circulation until it opened. However, hot coolant wouldn't ever
*reach* the T-stat to cause it to open, and you'd have a catch-22
situation. Also, allowing the coolant to circulate within the engine
(but bypassing the radiator) lets the engine warm up evenly rather than
having hot-spots form in the cylinder head.

2) Air evacuation. The bypass hose routed to the reservoir as is done on
many modern engines is the only way for the engine to expel trapped air
from the cooling system. That wasn't as much of a problem when engines
had radiator top tanks mounted higher than the engine and connected by a
hose that rose smoothly up from the engine to the tank, but nowdays the
cooling system plumbing is constrained by packing everything under a
low, aerodynamic hood so that its harder to evacuate the air from the
system.