They can be played together. If played on this way, you will only recieve the Catachan doctrine on your Catachan units. Militarum Tempestus do not block other doctrines, but will not benefit from their own.
Edit - I missed that there were 2 detachments. I think each should get their perks as long as the MT one is entirely composed of MT, ie no Catachans hanging around.
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