You may be deemed inadmissible. You could face inadmissibility for unlawful presence or other grounds depending upon the reason for the denial. Even if you are not inadmissible, you may have difficulty securing future non-immigrant visas. In addition, if your application is denied and you are placed in removal proceedings, but fail to appear because you departed the U.S., you could be ordered removed in your absence. If you are in a bona fide marriage and are concerned that your application for adjustment of status may be denied, you would be best advised to retain an attorney as soon as possible.
It would depend on whether you accrue any unlawful status before leaving, or the basis of the denial - for instance if there is a finding of fraud or a misrepresentation, then yes you could later be found to be inadmissible.
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If the government hasn't initiated removal then you can leave of your own volition. Whether you'd be considered inadmissible down the road would depend on facts leading up to your departure.
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I would need to get more details and see the reasons for the denial. It is very possible. It is also possible you could reapply or have other relief in removal proceedings. Do not make a decision without consulting with an immigration lawyer. You should do so as soon as possible.
Technically, if you were in F-1 status, you can't accrue "unlawful presence" because generally you are admitted for duration of status "D/S" unless your F-1 status is revoked be an immigration judge or DHS. Although you can't accrue "unlawful presence" triggering the 3/10 bar you may still be in admissible for failing to maintain your status in violation of the immigration law. That being said you may have other issues that need to be addressed immediately. I would seek an experienced immigration attorney to assist you in the process. Good Luck!