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If I was to put a squad of Thousand sons into my EC army, would it no longer be EC?

Nice avatar. Strictly speaking, no, since TS are mercs now, but it seems to lose a bit of its theme.

No, it would no longer be EC.
EC do not need Thousand Sons.

Well, the ultimate answer would be:
It depends. It depends on how close you want to match the old/new fluff. It depends if you are going to 'count as' stuff.

It's not too hard to make up a Slaaneshi background for a Dust Bucket-like unit.
They shuffle (S&P) and don't feel as much pain(4++) because they are so high on NOT combat drugs and have a different kind of sonic weapon.

But at face value...yes, adding TS to an EC army makes it a mixed force and not a pure list. It can still be an 'EC' army, but the TS will break up the theme if they are not 'count as'.