If Aliens (E.T) were profoundly deaf would their spaceships be very noisy and therefore very easy to detect

If an alien species had no ears and communicated by ESP, having no understanding of noise when they made machines, noise levels would not be a factor, 250 decibel leaf blowers wouldn't upset neighbours, a clock in the library that screamed like a banshee would be okay, so they could build a radar proof invisible spacecraft (since they have radar and eyes) that sounds like a Mother-in-law nagging you about watching the game when the lawn needs mowing, So instead of having radar dish arrays scanning the Cosmos shouldn't we invent a giant stethoscope to listen for noisy exhausts?

Possible. However, if they had any nerves in their bodies, they would likely feel the vibrations of certain mechanics. Ir would be up to their specific evolution as to weather that would be a nuisance or not... or for detecting faulty mechanics for that matter.

To me, it would seem unlikely that a species incapable of detecting sound could design a working spacecraft, imagine how difficult it would be to identify car problems in advance without hearing the problem first... every alarm in their society would have to be visual... not necessarily good if there is a fire while you are sleeping...

Of course, all of my points have counter-arguments, since it is impossible to know the historical evolution of a hypothetical species.

Still, we wouldn't hear them until they entered our atmosphere.

I know they say there's no such thing as a stupid question, but this sure comes close. How would anyone know the answer to this? If ET's are travelling the same way we travel, as in rocket ships, then I would imagine that they definitely make noise. However, any race capable of interstellar travel would necessarily be far more advanced than us, which would mean that they could very well have vessels that are silent and perhaps even "cloaked" or invisible.

I'm sure that a species that had achieved intergalactic travel would know what sound waves are even if they are deaf...

an inability to hear has no correlation to the sound volume emitted from what one such being constructs.

stevie wonder is blind; but that doesn't mean his socks don't match

Sounds do not travel through space.