Could the US Air Force ever replace the Thunderbird pilots with drones?
Tight formation flying can be done with stock aircraft and skilled pilots, but drones would need additional sensors and new code in their FCS. Also, you can fly aerobatics even with gliders, but only when a decent power-to-weight ratio is reached, aerobatics becomes a spectator sport. I think it is frivolous for the US Air Force to pay for the development and additional equipment to make drones fly aerobatic displays, but few Air Forces are known for an enlightened budget discipline. I expect, however, that this will be added first by a company producing drones, and for demonstration and marketing purposes, and then the taxpayer will fund this indirectly.

Formation flying was a needed skill for bomber pilots, back then when their bundled defensive weapons provided the best protection against fighter attacks, and aerobatic flying was and still is valuable for fighter pilots. In the days of missiles and UAVs, neither formation flying nor aerobatics are necessary skills anymore, so in a way aerobatic formations are a quaint relic from the last millennium.

To answer the "could" aspect of your question: No, not directly. This would need modifications to existing drones.

To answer the "ever" aspect: Once the services field UCAVs (unmanned combat drones) with a good power-to-weight ratio, having them fly aerobatic displays looks almost unavoidable, but I expect it will not be the Air Force, but the marketing department of a big contractor driving this.