It's a tough one, but I think the answer is yes, with a bit of care.
While the question is simply "Do invisible, undetectable beings exist?" (Or invisible pink unicorns the answer is basically "No, this is unfalsifiable. There's no way to collect empirical evidence. It is not something science could investigate." However, once the claim strays into the natural world, science can pounce!
- Thetans are manifest as lumps
Claiming that Thetans are represented by lumps on the body is also, at first glance, unfalsifiable. If it was not true, and the lumps were random, how would we know?
As soon as someone claims they can reliably detect them, we can do some studies.
e.g. Inter-rater Reliability (If the same person is presented to two different such people, do they give the same answer?) or Test-Retest Reliability (If the same person is presented twice to the same scientologist, do they give the same answer?)
If the answers to these are no, it suggests that they cannot detect Thetans as claimed. If the answer is yes, alas, it doesn't prove anything.
For this sort of test to be relevant, we need a claim from scientologists that they CAN do this. (e.g. if they claim was that Thetans frequently move across the body, it is once again unfalsifiable.) Your original question lacked such a specific claim.
- Removing a thetan as real world effects!
It depends what the differences are. If removing a thetan is a quick process makes you three inches taller or weigh 2 kg less, that would certainly be testable. If it makes you feel at peace or have more energy in the morning, it might be testable with an appropriate placebo control.
Again, a specific claim would be required, and your question didn't have one.
I think it is possible to ask a question about Thetans, but it won't be "Do they exist?" It might be "Does the process known as 'Thetan removal' make you 3 inches taller?" or "Are E-meters reliable between blinded testers?"