I can't offer any direct advice with porting the AC OnSale module. But I know what you are up against. I'm nearly done with doing that to Bill's Checkout One (one page checkout) module. It's been a horrible experience but I think I've finally beaten it.
You can get a feel for some issues by testing the module's php files using these online PH7 compatibility tools:
https://phpcodechecker.com/
https://www.piliapp.com/php-syntax-check/
As mentioned in the previous post, you'll need to recreate the missing mysql_real_escape_string() function. And I suspect there will be some instances of the deleted mysql_query() function (removed in PHP7). It can be replaced with db_query().
Be sure to work from a development store because it may take awhile to sort through all the problems that come up.
No doubt there will be more to it than these things. But if you post about the issues that pop up then maybe the community can walk you through it.
BTW, I'm using XC's Onsale Module (X-HotProducts) and it is working in my 4.4.5 store with PH7, no patches.