No H1 is required.
Rather spending a huge amount of money for 1st AC in Mahabodhi, anybody would take ticket in 2AC of Rajdhani express which would have less travel time as well as catering is present.
Mahabodhi was given 2 2A and 3 3A coach to match the CC of Gaya Chennai express so that it would be a backup rake for Mahabodhi.