i think it all depends what the arrest warrant is for. i have a friend who was served a deportation order last year and he traveled to chicago to attend the hearing. he went through airport security without any problem.
Flying in and out of the country definitely yes. Within the country - well if she is wanted by the FBI and on a most wanted list - maybe. Writing a "bad cheque" is generally not aggravated assault. And if she is going back for her hearing - she should bring the document.
No she would not be deported as a LPR and I know because I work in the area of Justice - and not as a secretary - and I have dealt with this before. But I have never written a bad cheque nor have I ever committed any crime which gives me the security clearance to do my job. Can anyone tell you if they will check for sure. No - why? it is all random. No one ever knows for sure who is checked and who is not. Why don't you phone the place where they issued the warrant and ask if she is on the list. ( I know LPR's who have committed much worse crimes and they are not deported.) Being a LPR gives you more rights than you think. Basically all you can't do is vote. You can be drunk and run over someone with your car and not be deported!!!!
If you are so afraid - get a second job and take the bus. (But there could be police at the bus station or the ticket attendant may have a list.oooohhhhh) Boy your friend must be mighty important.
I fly almost every week these days.. east to west coast. this week end going to PIT, PA for three weeks.
As per my experience if you book ticket within 24 hours of travelling time, computer generates special code so you have to go through special check ups. it can happend to anyone, including USC. Once you are in special checkup then only your name will be checked , otherwise you just only get checked up routinely which does not includes Flag checks. only baggage checks for certian items not allowed on plane.
TSA only checks the people in full screenings when you are stopped a side and first thing that send your ticket and boarding pass to Computer to check your name against terriorist List.