End of SDP gateway, hypothetical nul claim to ESAir before it ends

The SDP gateway ends on 27/01/2021. Is it possible, while waiting for the outcome of a PIP appeal, to put in a claim for ESAir before that date on the basis that while PIP is not currently in payment, it will eventually be backdated to cover the current period? So that any refusal of ESAir could be revised once PIP is awarded?

My case study is:
My working age client receives a private pension and used to get ESAir. Her pension increased and she was just overscale for ESAir so it ended. She was then awarded PIP SRDL. She could’ve, should’ve, made a new claim for ESAir on basis that she was now underscale due to SDP, and had SDP in her HB, but she never had advice about this. Her PIP ended more than a month ago and she’s now been referred to us, so we’re just outside the SDP gateway 1 month window for making a new ESAir claim.

Her PIP decision might not even get an MR done by 27/01/21, let alone an appeal! If her PIP isn’t back in payment by late Jan, could we make an ESAir claim before 27/01/21, knowing that it will be refused on basis of no current SDP, and then later on ask to revise the decision once PIP backdated to cover that period?

I don’t think so. Admittedly not sure on the regs, but if I recall, there won’t be a (n appealable) decision on her ESA claim - as she doesn’t fall into the limited category of people who can even start a claim. Slightly different if her HB has stopped, she might be able to submit a claim again, and ask the council to stay decision on her claim until after the PIP appeal.

But, she should be eligible for the transitional SDP element in UC once her PIP is reinstated and backdated. Provided there would have been SDP entitlement in her HB on the date she makes the UC claim.

On a different note - can she pause or reduce her pension? Or, in ther alternative - if she sought, and has been misadvised by her pension provider/adviser, causing her to lose her ESA, she could consider a claim against them for compensation. Wouldn’t normally think of this one, but just discussed indemnity insurance the other day.

EDIT: Reducing her pension now obviously doesn’t help.