Indeed it would. Stick with 304. Also best not to mix fittings/parts of different alloys, eg 304 and 316. I know they used different filler rod.
304 and 316 can both be welded with Type 308 filler metals. 304 can be welded with 316.
For the base question, 201 contains probably about the same amount of chromium as a cheap chinese made 304 does. With manganese replacing nickel it is known as the cheap man's austenitic.
From the Allegheny Ludlum website:
ATI 201 HP™ and ATI 201L HP™ can be welded by all conventional methods applied to 18 percent chromium, 8 percent nickel steels. Filler wire or electrodes of the conventional chromium-nickel analyses can be used. Like other chromium-nickel 300 series austenitic stainless steels where carbon is not controlled below 0.03%, ATI 201 HP™ alloy is sensitive to intergranular corrosion in the weld heat affected zone.