Insofar as we can, we are commanded to obey all legal authorities; within the realm of their authority.[1] Now, whether or not laws concerning marriage are within the realm of the authority of the state is a question worth discussing Biblically; especially now that the state has begun to legalize sodomite marriage. However, be that as it may, in most states the laws concerning marriage are flexible enough to permit Biblical marriage.

First off, there is as of now no law that forces people who ‘live together’ to be what the state calls ‘married’ (and what a perversion of the Biblical Law this is). With what we call ‘married’ differing in so many respects from what the State calls ‘married’, and even differing from state to state and country to country; is it even useful to apply for state ‘marriage’?
Secondly, in many states, ‘living together’ and calling yourselves ‘husband and wife’ in front of witnesses constitutes ‘marriage’.
Thirdly, I know of no laws concerning ‘betrothal’.

All this considered, there would likely be no legal obstacle for most betrothals. However each father would need to investigate the legalities in their jurisdiction, and would need to come to the betrothal with the proper information in hand.