Incorrect.
Just for discussion's sake, if I have a left x-wind and I push on the right rudder pedal while my C-182's nose gear is still on the ground, I'm headed for the right side ditch. Period. There's a whiffle tree and a bungee cord that are going to make sure I do.
I'm not "using it as a crutch", in regards to the nose gear. I'm explaining (because the original poster specifically asked about a Cessna 182) that up until the point enough weight comes off the nose gear and the strut extends all the way downward into the centering cam, right rudder is not correct.
You can't do it because you have nose wheel steering up until that point.
He asked about a 182, so I'm explaining the 182's systems. This falls under: Know your aircraft.
As soon as you get the weight off the nose gear, and once it falls into the centering cam and the nose gear isn't pointing to the right anymore, then you're correct. Then you can apply right rudder.
That happens at rotation speed unless you're doing soft field takeoffs in gusty cross-winds and holding the nose in the air. If he's doing that, good luck.
Unless you're at some crazy DA and weight loading, a C-182 doesn't exactly loiter near the ground after liftoff. That transition from runway to flying happens plenty quick.
Anyway, at rotation and liftoff in the 182, by the time you apply that "immediate" right rudder at liftoff, you're going to be taking it right back out to allow the aircraft to weathervane into the crab, because otherwise you're going to be blown downwind.
Have you flown the 182 much? Grab the POH and play along here...
*Published* rotation speed is 55 knots. Vx is 65 knots. At 55, you will start to climb off the runway, but you still have 10 knots to gain after rotation if it's done at the published speed. (LOTS of people don't lift the nose gear at all, which is sloppy, for a normal non-gusty non-crosswind takeoff.)
Assuming our OP isn't sloppy with his 182, the CHANGE in a gusty crosswind is to go ahead and leave the nose gear on the ground for another 5 knots or so.
He was asking about DIFFERENCES from a normal takeoff.
My point to the original poster was that in the 182, you don't *have* to lift the nose wheel off at 55 in gusty conditions. Let it help with the x-wind a tiny bit longer.
Leave it on the ground until 60, then rotate. It'll probably hop off the runway all three wheels simultaneously at 60 knots anyway. It's ready to go flying.
(My 182 with the STOL kit is ready to go flying and can start "hopping" at about 45 MPH - not knots, MPH -- indicated. You're WAY behind the power curve there... but we can REALLY use the ground-effect tricks. I left our numbers for our aircraft out of this discussion, since he's flying a normal 182.)
Depending on load and headwind, you're not even going to be able to count to one before you accelerate from 55 through 60. This is SUBTLE stuff we're talking about here.
You almost have to watch someone ELSE do it and stare at the airspeed indicator to see it. You feel it under your butt more than you stare at the numbers on the ASI.
Should I say it? Duh. When did the OP ask about traffic patterns?
More pattern stuff. Wasn't his question. He specifically asked about crosswind TAKEOFF techniques in a C-182.
I got no impression he didn't know what a crosswind (or any other wind) does to his pattern work.