Damage to a bike resulted in a broken hanger and a damaged derailleur. I can't get hold of a like-for-like replacement derailleur (Alivio M410). Have seen others state that a 9speed derailleur will work on an 8speed cassette but want to check if this is the case and if the Acera T3000 (which is marketed as 9 speed) will work
Yes, the chain should be able to clear the cage and the pull ratio is the same.
There could be also incompatibility in the ability to wrap a chain of certain gear ranges and in maximum and minimum sprocket sizes. M410s were available as GS (medium cage) or SGS (long cage), T3000 is SGS (long cage). It is not clear which one you had, but you should be fine with T3000. You may need to adjust the length of your chain.