Yes, you have correctly analyzed the situation, and there will be reflections. But you ask if there will be any loss.
Reflections don't cause loss directly; they just traverse the same piece of transmission line many times and the loss in the line adds up. (Or to take a sum-of-all-the-reflections perspective: They cause increased current in the transmission line (relative to what's going in and out the ends), and therefore additional loss due to resistance.)
Another effect of reflections is to add a time delay to part of the signal, like multipath, but this rarely matters, and it is not loss per se — all the energy in still goes out.
So, “neglecting the practical terms such as attenuation”, there is no loss, but in practice there is. You can reduce the coax loss by minimizing the length between the stub and tee, of course.
What would theoretically make sense here is a tee with two 50 Ω ports and one 25 Ω port, but those don't exist since they'd need specialized connectors. Instead, you would build a custom matching circuit which just keeps everything inside as short as possible or, for higher frequencies, has impedance-matched PCB traces.
Note that what you're effectively building here is a power divider (a.k.a. splitter in cable-TV land). Therefore, you could purchase it as a standard part instead of building your own, and it would be already designed to minimize reflections and loss. Then the worst problem you'd have is the 57 Ω - 50 Ω mismatch.