I managed to successfully bleed a Shimano hydraulic brake but used an improvised kit instead of the official Shimano one. Since I used a regular syringe instead of the funnel+plunger system which may guarantee a certain oil level in the master cylinder reservoir when used properly, I was wondering if the oil level is the master cylinder reservoir is critical.
The system is designed to have the lever bleed screw displace some oil as it's reinstalled. In other words, the lever end wants to be completely full at the end, and there is not supposed to be an air gap there
In the too little fluid direction, there is some tolerance for an air gap before symptoms begin, but ideally you wouldn't have any. If by chance you finish the bleed and find out there to be a small air gap at the lever, if it's small enough then dripping a little oil in may be reasonable, but usually there's none when you pull off the funnel so if someone does wind up with one, it would first make me worry that something went wrong in the bleed.
If one doesn't have a funnel, then most of the time, doing the "gravity bleed" part of the procedure the same way as with an older Shimano brake works fine, i.e. by dripping in more fluid in the screw hole as the fluid feeds into the catch bag/bottle at the other end. Doing this with road levers would be clumsy at best though, as they tend to often really need to have their angular position changed during this step to free up air bubbles, as per the official instructions.