(Another) Multiple HAT Question

Yes, Pan/Tilt HAT uses just i2c, which is a 2-pin data bus it would happily share with Explorer HAT.

Be careful reading an HC-04 alongside these devices, though, since the overhead of both Python libraries could lead to unreliable timings and results from your distance sensor.

It’s more expensive, but I would personally use something like this: https://www.adafruit.com/product/164 since it’s much easier to work with.

That said people have got it working;

See: Unreliable HC-SR04 with Explorer HAT Pro