Yes*
In a detachment, everyone needs to share a keyword. They all have the imperium keyword, so you are good.
That said...
In the new SM codex, you only get some of the spiffy bonuses if everyone has the same <chapter> keyword, which the inquisitor would not.
But then...
You can still have multiple detachments in your army, so could have one of SM, and one of “other”, and your whole army would work just fine.
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