I\'ve recently started learning SWT (on class #4, to be precise) due to business requirements, and previously I had been developing with Swing for 2 years.
We deploy
SWT is not Eclipse-based, but the Eclipse UI is SWT-based. Eclipse uses the SWT library for its drawing. It is used a GUI library from the Eclipse consortium, available for many systems. If you want to deploy your normal Java Application with an SWT GUI you just add the corresponding libs and .dll's or .so's. Therefore, everything you can do (deployment) with Java respectively speaking Swing, can be done with SWT, if you provide the according libraries. There are tools and ways to compile everything into .exe's but that is not necessarily needed. I do not really get the Eclipse EXE thing you are talking about, but eclipse just provides a starter exe, which is basically just a wrapper. Otherwise, some people refer to Eclipse RCP als Eclipse EXE but this is not correct. You CAN use the Eclipse RCP to base your App and this would use SWT as UI library. But you can use SWT all by yourself just as library without the Eclipse trail.
I hope this helps.