Hell Yeah!

Synchronizers perform two functions-- engage the synchro in one
direction and then lock one gear to the mainshaft.

Engage the synchro the other way and it disengages from the first gear,
passes through a neutral position, and engages a gear on the other
side.

If anyone is a tranny expert correct me if I'm wrong but wouldn't the
vehicle have trouble staying in gear also if it was a sychronizer
problem?

There may be some adjustment problem with the clutch and I have heard
that transmission fluid that is not compatible can cause such problems
also. Some people put automatic transmission fluid in a manual tranny
which seems it would be too "thin" and slippery to me because I think
of a manual transmission as being "thick" as gear oil should be.

My two cents says it could be caused by other things besides
synchronizers.