The player can certainly initiate sieges and build rams with nothing but horse.

I do this all the time, particularly with HA armies. Sometimes I bring ram pushers up later or hire mercs to push the rams after they are built. Sometimes the AI will sally and I will win without bothering with infantry.

Since it is possibe to take a city before starving them out this way (or with a spy), it's not necessarily a bug.

However, the AI does not tend to sally early when the odds are not in its favor, so I wouldn't expect it to lose a lot of sally-before-the-last-turn battles on autocalc.