If I have the Adobe suite on my Mac book air, and want to transfer it to a new Mac desktop, is that possible with the migration assistant?

If it is a 64 bit version yes it may work. You may need the securities keys that originaly came with the Adobe suite. Please carefully read Setup Assistant and Migration Assistant to learn the correct method of migrating. If your new Mac has not been turned on yet, please follow the Setup Assistant instrucitons. Also, if you do not have a Time Machine backup of the MBA then create one. You will need an external HD (many experienced users prefer the OWC Mercury Elite Pro) and follow the Apple's instructions in Back up your Mac with Time Machine.

You really need to deactivate it with Adobe on the old system, then re-install it and activate it on the new one.

You can move the data with Migration assistant, but Moving the Creative Suite itself is not going to give you good results if it works at all.

It is important to know that Migration Assistant transfers all or no files. You cn not selectively transfer any files. As noted, I would reinstall it.