100%. In fact 'people who immigrated illegally' is fine, as illegally refers to the action of immigrating and not the person.
Maria is an illegal. - bad
Maria is an illegal immigrant. - bad
Maria immigrated illegally. - no problem
Maria is not a legal resident. - no problem
Maria is undocumented. - no problem
The caps are a little off-putting, but I suppose it works.
I don't personally like it though. If someone is a legal alien (work visa, not naturalized) and is guilty of some other crime are they a criminal legal alien? mostly joking
Undocumented alien or undocumented immigrant identifies the actual crime so I would use that myself. But I wouldn't correct you on it - I know what you are trying to convey and it is accurate if imprecise.
"UNDOCUMENTED IMMIGRANT" ISN'T ABOUT OPEN BORDERS OR
SAYING NO CRIME WAS COMMITTED. ENTERING THE COUNTRY
ILLEGALLY OR OVERSTAYING A VISA IS A CRIME.
"ILLEGALS" OR "ILLEGAL ALIENS" IS DEHUMANIZING BECAUSE IT
IS POOR ENGLISH.
ACTIONS OR OBJECTS CAN BE ILLEGAL BUT PEOPLE AREN'T.
EVEN PEDOPHILES AND RAPISTS AREN'T SIMPLY CALLED 'ILLEGALS'.
DON'T WASTE TIME CORRECTING PEOPLE OR BRINGING IT
UP FIRST, BUT IF THEY DO, THIS IS WHY WE SAY IT THE WAY WE DO.