You can have two (or more) separate petitions with USCIS.
For example, if you get sponsored by an employer for a green card and you marry a US citizen, you might ask which green card should you pursue? The answer is both. This is fine and encouraged.
This also comes up with people who apply for asylum. This can take years to adjudicate. What if they get married to a US citizen in the meantime? Generally, the advice is to maintain your asylum application AND apply for your marriage-based green card.
This doesn't just apply to green cards either. If you work on an H1B, it's completely fine to apply for a green card (through employment and/or marriage) at the same time. Some will point out that the H1B is a so-called dual intent visa that doesn't preclude immigrant intent but that's not really what that means because you can adjust status to a green card on a non-immigrant intent visa too.
"Immigrant intent" here really means if a consulate will issue you the visa overseas and if CBP will let you into the country if you've shown immigrant intent (which usually means filing an I130 or similar). Once someone files an I130 for you, you'll not be granted a student or visitor's visa from outside the US and if you have either, you might be denied entry at the border. Because those aren't dual intent visas.
A red flag for USCIS for visa fraud is applying for an F1 visa, coming to the US, stopping studying and getting married. To them it looks like you committed immigration fraud just to come to the US.
That's why I say you should continue your studies (and also not get married in the first few months upon entering the US on a student visa).
So there's really no studying out of status per se. If you continue your studies, your F1 is still valid. When you get your EAD or green card, you can study with that and terminate your F1 status.
If you fall out of status on an F1 for a certain period of time it might be difficult or even impossible to resume student status to study at the same or another institution. I'm honestly not familiar with the rules around this.
But you're just not really going to be studying in the US without any status.
Just for the record I went through this process this year with my spouse and a lawyer. My spouse did continue studying and had their i-130, i-485, and i-131, however the immigration office told our lawyer and said their F1 was no longer valid and that my spouse was under “authorized stay” not a visa any longer, especially for i-131.
For example, if you get sponsored by an employer for a green card and you marry a US citizen, you might ask which green card should you pursue? The answer is both. This is fine and encouraged.
This also comes up with people who apply for asylum. This can take years to adjudicate. What if they get married to a US citizen in the meantime? Generally, the advice is to maintain your asylum application AND apply for your marriage-based green card.
This doesn't just apply to green cards either. If you work on an H1B, it's completely fine to apply for a green card (through employment and/or marriage) at the same time. Some will point out that the H1B is a so-called dual intent visa that doesn't preclude immigrant intent but that's not really what that means because you can adjust status to a green card on a non-immigrant intent visa too.
"Immigrant intent" here really means if a consulate will issue you the visa overseas and if CBP will let you into the country if you've shown immigrant intent (which usually means filing an I130 or similar). Once someone files an I130 for you, you'll not be granted a student or visitor's visa from outside the US and if you have either, you might be denied entry at the border. Because those aren't dual intent visas.
A red flag for USCIS for visa fraud is applying for an F1 visa, coming to the US, stopping studying and getting married. To them it looks like you committed immigration fraud just to come to the US.
That's why I say you should continue your studies (and also not get married in the first few months upon entering the US on a student visa).
So there's really no studying out of status per se. If you continue your studies, your F1 is still valid. When you get your EAD or green card, you can study with that and terminate your F1 status.
If you fall out of status on an F1 for a certain period of time it might be difficult or even impossible to resume student status to study at the same or another institution. I'm honestly not familiar with the rules around this.
But you're just not really going to be studying in the US without any status.