it could well do. The engine i had that problem with is now fitted to my cabriolet. In the previous car even though it only ran low boost it felt rapid and i think this was the cause, the wastegate leaking made the boost come in later but harder, it boosts like a turbo diesel now u can barely drive the thing down the road without it spooling up.

So yea it could be possible but the only way you're going to find out is by trial and error.

if the housing is cracked though it will be obvious to look at when you drop the elbow off.