Is drilling a pilot hole into the plaster wall of an old house hazardous asbestos?
It is difficult to say

If you are concerned about asbestos you need to go to your local council and tell them you are concerned about your walls being filled with asbestos. They can check records if any occurances of asbestos builds exist in your area. even if nothing shows up it will be worth doing an independent test if you are still worried.

There are asbestos tester kits available also for DIY- but be advised to wear asbestos protective masks and clothing- if it turns out positive you will need to deal with it asap.

If they find asbestos.. well you need to tell the council and there should be grants available to remove it.

Be careful and wear certified masks and gloves at all times during testing and never reuse any of the kit- dispose at once into bag- into separate container. IF tests reveal negative your stuff can be dumped into normal channels.. IF positive you need your council to collect it and incinerate all exposed items.