Royal Caribbean considers each cruise as an independent cruise. Separate booking number is given to each one whether B2B or B2B2B2B...2B.
On our last BTB, we had checked in for the second leg. On turn around day they asked us for our room number and gave us our new keys (Set Sail Pass). The couple next to us had not done the check in and had to got through all the steps, Credit Card, Pictures, etc. before they received their room key.
So, is it mandatory, no. Does it save you a few minutes - yes. None of us doing the B2B were taken to the off ship holding area until everyone had been processed, including the family of four that showed up late.