Can Apple Motion export with alpha to bring into iMovie? I currently use After Effects / Premier Pro at work. For my home use I need a new laptop and am considering a Mac. The deciding factor will be cost and if iMovie/Motion can do what I want.

(I'll probably eventually get Final Cut but its going to be a while due to budget)

If I use Motion to create lower thirds, title sequences, and playing a bit with other special effects like particle systems and such... afterwards can I export them with a transparent / alpha background to import into iMovie?

I read How useful is Motion 5 without Final Cut Pro X? but it doesn't really cover this. Says I would have to slice up the movie and do the Motion work on top of the exact segment I want it.

Until I can afford to upgrade to FCP would Motion and iMovie give me the tools I'm looking for?
Yes, Motion can export with transparency into iMovie. I have used this exact procedure in the past and can confirm it works great. Using iMovie's picture in picture with some resizing retains the alpha and lets you overlay whatever you've exported from Motion into iMovie.

The linked question's answer is from 2011 and things have changed a lot since then, namely the introduction of the 'Advanced Tools' which include picture in picture (and have recently been abolished and integrated directly into the workflow). This means you don't have to 'splice' your video and work on it externally — it's all integrated pretty smoothly.