I've done some playtesting against Hojo and am of this opinion:
1. The AI is still allowed to deficit spend (reportedly until patch 1.13 comes out) on the more difficult levels.
2. Hojo purchase troops every turn in every province that contains troop training capabilities.
3. While the Hojo AI hasn't, according to my reading of the saved-game campaign log, deficit spend to purchase buildings and upgrades, it will do it to train troops.
4. This is how it is able to support such large armies that even the richest clan could never afford to accomodate (1 soldier=1 koku spent in retainer per year). Hojo simply spends to produce regions with troop-producing capabilities, and then starts cranking out men when the money runs out. Sometimes Hojo goes bankrupt when all he's capable of producing are Ashi, or most of his provinces can only produce Ashi, while other times he gets lucky and is able to upgrade to Monks etc. before his bankruptcy hits. This explains the general unbalanced nature of his armies.