I was working on my prize 300D 1985 at my brother's house.
On top of it I was very tired.
All I had was a bottle jack and I jacked the car up using the Cross Member directly behind the oil pan drain. I had to jack it pretty high and the car slipped. One side slipped off the Passenger Side jack stand and the stand tipped and hit deeper in a body cavity near the exhaust.
The driver side of the car hit the ground.
Worst I really dented and deformed the Cross Member.
The car which I recently aligned, tracks a little to the left now, but that might be my imagination.
Do I need a frame alignment?

The alignment will be inevitable in your case, but I would be more worried about the damage to the crossmember than just the alignment issue. If the damage is as severe as you claim, a crossmember failure at highway speeds could be catastrophic! Needless to say, the crossmember damage may render an alignment useless.

Do search the threads for tips on proper car jacking to prevent mishaps like that in the future! I'm glad you weren't under the car when it slipped!

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car

Most every alignment change will alter the position of the steering wheel. If the steering wheel is no longer straight (or whatever way it was before) I would realign it.

Any change in component position will affect toe-in. Toe-in will not affect the way the car drives (unless seriously toed out) but small differences will wear tires tremendously.

I doubt that you can seriously affect the integrity of the cross member my just denting it.

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Steve Brotherton
Continental Imports
Gainesville FL
Bosch Master, ASE Master, L1
33 years MB technician