Not really likely (or doable). In Spain the person of the queen was sacrosanct, and all the court knew it. The king was the only one allowed to touch her. Spain had a bad experience with la Beltraneja and didn't fancy a repeat.
The POD was set in 1700, namely that the Austrian candidate wins the WotSS. Now, the only way that's gonna happen if there isn't a hope in Hell of Carlos III succeeding to the imperial throne. So, either Empress Wilhelmine needs to die (and Josef remarries to someone who gives him a surviving son) or her son needs to live or one of her daughters is born male.
With a healthy grandson (or at least the prospect of one) Leopold might not promulgate the Succession Pact. When he set it up in 1703, the situation was Wilhelmine couldn't have more kids, Josef's son was dead, and Karl was off campaigning in Spain (unmarried and childless). In TTL he's perhaps not as despondent (unless Josef's already remarried and the new wife hasn't conceived yet or is too young or whatever).
As to Elisabeth Christine, IDK what the reason was for her and Karl's late start. Her brother-in-law, the tsarevich despised her sister and yet still managed to knock her up pretty soon after the wedding. Karl and Lieschen took 7years. Now if you wanna make the argument there's a war on and they aren't together all the time, Felipe V and his first wife managed 4 kids between 1707 and 1713 (four years and they're a lot more related than Karl-Lieschen). 3 of those kids would've been conceived before the treaties were signed. So, if we're gonna say Elisabeth Christine failed in Austria, I think her husband at least gets part of the blame. And besides, there's another four years (1711-1715) where Karl was apparently not getting his wife preggers - why I don't know. If I knew I was the last guy in my family and I needed a son(s), I'd be going at it like a rabbit with my wife (who looks like the 18th century's version of a Victoria's Secret model) in the hopes of fathering one. Hell, I'd probably be doing that even if I didn't need a son. Not doing god knows what Karl was doing between April 1708 and July 1715 and then again between September 1718 and July 1723.