Can I connect to it from a plane?
Right now? No. Starlink does not work directly with cellphones or laptops etc. There's an external dish you need.
You probably could get Starlink working on an aircraft, but you'd need an aerodynamic RF transparent radome on the outside that would allow the starlink antenna to swivel and point at the satellite as both you and the satellite move. Starlink service needs an antenna that looks like this. It's powered and it moves to track satellites across the sky...
https://youtu.be/cU2y-QmQfXYSo in theory, yes, but in practice, not without some major design and engineering to get it implemented. There's also going to be programming and firmware needed, since I presume the Starlink system and it's tracking is currently optimized to work from a fixed ground position.
And I'm no engineer, so I don't know what the orbital specs of the satellites current commercial aircraft with in-flight internet service use, so the radome covering the Starlink antenna might need to be taller/bigger to give it enough vertical deflection which then could cause problems mounting it on the airframe. I don't know if the internet satellites that currently service aircraft are geostationary or what. If they are, that simplifies things for the current setups in use since obviously it's position in the sky won't change, and they can use an antenna that's optimized for only horizontal rotation, and the antenna is set to cover the sky in an angle covering for the height of the satellite based on it's elevation in the latitudes the airliner is expected to operate at.
Starlink uses many more satellites that are constantly moving across the sky. Which means the antenna needs to be a lot more active to track them.
From watching teardown videos, I do know that the Starlink antenna is a phased array. So maybe it's possible to cut up the array and make it into little tilting tiles, so the array only needs to spin on the horizontal axis and the individual tilting elements can track the satellite in the vertical azimuth above the horizon. And that would allow for a smaller/flatter radome. But again, Starlink would need to cooperate with such an endeavor on their end too.
I would hazard a guess that Starlink will address the boat, RV, and aircraft Internet markets in some way sooner or later. However we'll have to wait for them to release products and antennas optimized for it.