my rule of thumb on this one is:
if it had struts and aluminum cover then yes run it(77-up)
gm put struts on them for some reason i guess to reduce vertical downwards stress on front of tranny case,, even with support under t case,,, wierd.. you would thnk that would be plenty suppport..
if no struts(76 older and especially 72 older iron ones) then dont, unless you drive where mud and water is at,
i never run any dust shield covers on anything but then i dont have 4x4 or s-series 2wd strut kinds to drive, never have..
ive had cars with plastic shields, and mainly all 2wd trucks from the 80s and back to into the 60s, and i never run the shields on them, i always remove them it is one of the first mods i do to them when i first get them, i dont have a sheild on the 84 c-10 3 speed or the 72 dually c-30 465 and tey are staying that way and i wont have any trouble ever out of either, just like all the others in the past, auto or manual,
i toss them or sell them all and leave them open and never had a lick of trouble with any ever at all. no water no dirt no anything issues.,
everyone will have an opinion on this one, it may be funny
i say if with struts then leave it on, if not then remove it unless mud or water driving conditions,
so if your th350 doesnt run struts then id say screw it, no worries,
good luck