It is tricky subject but you can only know that once you apply B1/B2 visa. How US know when someone exit the Country, is from information from official source, such as POE, Airlines. If you exit US through Roxham, then will know after Info Pool Query. But i guess exit for Asylum purpose shouldnt be an issue when you reapply, but it depends on VO processing your application. I saw this one from US CBP
There is no regulation that requires a traveler departing the U.S. to exit through an open port of entry staff with CBP Officers. However, if you are exporting goods from the U.S. (i.e. a car or vehicle) you are required to depart through a port of entry, so a CBP Officer can verify you are the owner of the vehicle. Also, if leaving the U.S. by land, both Mexico and Canada require you to enter their countries through official ports of entry, so although you will not necessarily be breaking U.S. law to exit the U.S. anywhere you wish, you will immediately run in conflict with Mexican or Canadian law if you do not enter through a legal port of entry.
Prior to leaving the U.S., you should consult with the country you are traveling to ensure you met all of their entry requirements.