she sure can, if she has credible fear of returning back home, then she can tell that she did it to escape her country.
because i know someone who did that, but did not had any problem but his case was weak and he could not present fear of persecution and was denied.
but asylum process does not care how you enter the country legally or illegally, if you can prove that you have huge problem back home and you fear of your life, yes you for sure can apply for assylum, i am 100% sure about it. but your case will probably be heard by immigration judge instead of immigration officer. but again if case is strong there is no problem how you enter the country.