http://www.cdc.gov/ncidod/dbmd/diseaseinfo/hansens_t.htm
This CDC summary doesn't say anything about "highly infectious". It's bacterial, yet they've NEVER managed to get it to grow outside a living animal, so you can be pretty sure it's not growing on public toilet seats. Transmission is difficult (a lot like getting warts) and appears to require prolonged exposure. And about 95% people are flat-out immune to it (i.e. they can get technically "infected", but will never develop any symptoms of the disease). It is curable, but that takes a long time. Making it go dormant (and thus non-transmissable) is much quicker (about 3 months).
And the mode of transmission is ....?
You take your chances with it if you like. I, for one, prefer the legal system's requirement of at least a minimal standard of healthiness and vaccinations for each immigrant as a precondition for admittance into these United States.
IMO, those who steal their way into the US and are discovered carrying disease ought be treated as though they would be carrying deadly weapons and prosecuted likewise, with their host country billed for care and/or incarceration.