Hi,
The sentence would be “Já não tenho médica de família ela está grávida e ausente de baixa até ao fim do ano”? I guess not. You say “to remove “pois” and also the comma after it if someone writes it.” so was there supposed to be a comma after pois? But if both pois and the comma are removed and the result is as I showed above, at least, in Brazilian portuguese, the sentence is odd.
Ah ok! Well, for me, the absence of pois doesn’t affect much this sentence but we should see the effect in other cases, so it is worth proposing the rule.
And if possible and if it makes sense to you, a rule to flag pois between two commas. In the sentence above, “Já não tenho médico de família, pois, ela está…” is awkard. It is licensed in cases like “Eu quero descansar, pois, amanhã, terei muito trabalho.” where something after the comma (pois,) also has a comma (amanhã,). The comma after pois would appear not because of pois but because of the expression following it, that should be between commas.