In theory, for me to drill 0.1mm I require about 96,000 rpm , and at that sort of speed and with carbide drills you can almost disregard what material you are drilling.
But of course although speeds like that can be reached (at a price), if you are very careful with setups and runout, and if you are not too heavy handed, you can 'get away' with much lower speeds.
I was given a high speed, high precision drilling machine a little while ago. It will only reach 6,500 (I think) as it stands, so I am going to try it first. If I do suffer heavy attrition rates to my drills, I can quite easily modify to run up to just over 10,000 rpm. It is the speed which gives the drill it's strength to withstand the bending forces that break them, centrifugal force keeps them straight and rigid, but if you have too much runout, even the act of turning fast can snap the drill. HSS are better at withstanding runout, but I couldn't find any cheap ones in the sizes I required.
0.02mm (0.001" approx) is a lot of runout when it comes to tiny drills.
All I can say is try your mill, if it works, great, if not, you might need to make a drilling machine, as I was doing until I was given the one I now have (not too difficult), or get someone else to drill them for you who has the equipment.
My donated drilling machine with drill mounted

What a tiny drill looks like. The chuck is the smallest Albrecht do, it holds up to
1/
8".

Compared to normal small drills

The one on the right is 1.5mm diameter, on the left, 0.5mm (0.020"). The one I will be using in the middle, roughly twice the thickness of a human head hair.
Addition - Imagine a 1/2" drill having the same ratio runout as the one I will be using. If the runout at the tip is 0.001" and my drill is 0.004", then that equates to having the tip of the 1/2" drill wobbling with 1/8" runout. Now you can understand why runout, or lack of it is so important.
Bogs