Be honest up front ... not doing so will not end well.  You will probably need to file a joint return for her immigration paperwork so you will have to let the cat out of the bag eventually.  Also if you are married it can affect your scholorship eligibility or other such things.  

But to answer your direct question ... if you don't file a joint return and otherwise qualify as a dependent then yes your parents can still claim you. 

As far as taxes are concerned for now, as long as you are a student and under 24 your parents can claim you as a dependent if you file as married filing separately and you indicate on your tax return that someone can claim you as a dependent, and you meet the other requirements to be their dependent.

But this doesn't sound like a good plan. Sooner or later your parents are going to find out that you got married. One of the requirements for them to claim you as a dependent is that you live with them for more than half the year. If you and your new wife establish a household together, you are no longer living with your parents. If you don't live together, immigration is going to figure it out and decide that it's a sham marriage. Then you and your girlfriend will both be in trouble with immigration, and she will probably end up being deported.

If you are serious about getting married and staying married for the long term, you might as well tell your parents now because they are going to find out eventually. How do think they will react if you don't tell them, and they later find out that you have been married for a few years? On the other hand, if you are just getting married so your girlfriend can stay in the country, immigration is going to figure out that it's a sham marriage.