Not too small but yes. Typically three to five large auxiliaries. They also provide electrical power when the main engine isn’t running and during manoeuvres, and are always on standby.
Another issue I read about - you have ships sitting there waiting that were not intended to be sitting offshore for this length of time. Some were running out of fresh water and the ports really didn’t have the infrstructure to shuttle large quantities of supplies out to anchored ships, or the facilities for fully loaded tankers to re-dock to take on supplies. Not to mention, the month some have been waiting at anchor is about the length they would have been underway, so they may be reaching the end of food supplies too. So apparently there’s a serious logistics problem over and above starting the engines. Also the Gulf states are not keen to have large numbers of third-world crew wandering their cities on shore leave, even if the crew could afford it, so they’ve been stuck on those ships.