Yes and there is an ongoing problem in the east of the Indonesian island of Java where a “mud volcano” has erupted. It started two years ago and hasn’t stopped (Google “Sidoarjo”) and has now covered many square miles and is really devastating the area. There was drilling work going on at the time by an oil company and they have pretty much been universally blamed for the problem, they say however that their work was not the cause as the eruption occurred a little distance away from their borehole and the cause might be related to a nearby earthquake around the same time.
For most people it has been accepted that the drilling was the cause of the eruption and have refused to accept that it could have occurred naturally and that would appear to have been an end to it. However only last week in another spot in Indonesia hundreds of miles away on a separate island another “mud volcano” has erupted, no drilling was going on nearby. Not unnaturally the much maligned drilling company is pointing to that and saying “See?”.
So it’s hard to say definitely whether man made events can cause these tectonic problems.
I have often wondered about the unintended consequences of geothermal drilling, the deep kind that is.
It seems to me that a very deep drill could some day be a conduit should magma make it to the bore hole.
It's probably not likely, but it could happen.