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The toxicrene's "Hypertoxic Miasma" ability says that units within 6" take mortals. the "Suprise assault" detachment ability in the subterranean assault detachment reads as so:

In the Reinforcements step of your
Movement phase, when you set up a unit
on the battlefield from Reserves, you can
set that unit up wholly within 9" of one of
your Tunnel Markers and more than 6"
horizontally away from any enemy units.

If I set up my toxicrene as close as possible to an enemy unit, will that unit be within range of my Toxicrene's Aura?

No, cause your toxicrene be 6" away from enemy unit. So enemy unit doesn't be within 6.

Nope. More than 6” means that anything that requires you to be within 6” is not in effect.
Same with normal Deep Strike and any 9” effects.

 kabaakaba wrote:
No, cause your toxicrene be 6" away from enemy unit. So enemy unit doesn't be within 6.

To be 100% clear, a unit exactly 6" away is within 6" of a unit. However, since you must setup more than 6" away from any enemy units, you cannot be within 6" of that unit.