I haven’t tried that myself, but I would imagine not; I think what happens when you import an MB file is that Unity looks for Maya on your system, calls it up with just its command-line interface, and tells it to export an FBX. I don’t know if LT has the same sort of command-line interface stuff that regular Maya does (I know it does do MEL at least), so it’s possible they either haven’t added support for doing whatever Maya LT would require, or Maya LT just has no way to do it.
Either way, I’d personally recommend always exporting FBX files out manually, since if you ever need to move to a computer that doesn’t have any Maya installed at all, you’ll be out of luck on importing them. At one point, I also had some problems occasionally where the files didn’t import entirely correctly, but it’s been a long time since I tried it so that might have been fixed by now.