Technically yes, a woman can be named as a player in the team line up. (The rest of the information below is completely my opinion.) However, it is likely never to take place due to the obvious physical nature of football, especially in the english premier league. Also no team wants to lose at any time in the league so they're unlikely to field a player unless the player has had a chance to regularly train with the team, which is difficult since the best women players are training with their respective teams for the women's league as you mentioned. You are more likely to see a woman feature in a friendly game I guess.
Ah, unfortunately there IS an explicit rule against mixed gender teams so no, a promoted side couldn't sign any top female players
This absurd rule was tested in 2004 when Celaya, a Mexican Second Division team attempted to sign Maribel Dominguez a star of the Mexican Women's team. But FIFA blocked it Woman barred from men's football
In England, the FA has recently voted to extend the age at which "mixed gender football" is permitted, from 16 to 18 years FA to raise girls' football age limit
According to this Netherlands and Switzerland allow mixed gender football until 19, Germany and Italy at 17. Bear in mind this doesn't just apply to professional football, but to any organised matches at all under a league structure. So girls and guys can no doubt have a kick about in the park, but can't play together in any organised league at any level
So it seems possible that, in England at least, should a star female footballer be identified at an early enough age, she could in principle play for a professional men's team. Until she turns 18. Then no.