Presuming those off flavors come from either a bacterial infection or some wild yeasts mixing with your yeast strain, then Yes, it will be transferred to subsequent batches. However, if the "off flavors" come from skunking from light exposure or oxidization of fermented wort, then no, yeast washing would be fine. For me though, I wouldn't risk my next batch of beer on suspect yeast.
Currently On Draft: Bamberger Rauch Dunkel, Belgian Blond, Pilsener Urquell clone, Smoked Porter
Bottled: Concord Pyment, Mi'Apa Sparkling Mead, Chimay Blue, Old Simcoe American Barleywine, Old Cantankerous
Fermenting and Conditioning: Pseudo-Decoction Munich Dunkel, Left Hook Bitter
Recently Kicked Kegs: Fresh Hop Pale Ale, Citra Rye IPA
On Deck: Old Rasputin, Northstar IPA, Ur-bock Dunkel