First, I must say if you are running Lion you shouldn't worry about this, as all Lion machines have a "Restore Partition". That is they save all the system files required to restore the system on a special "section" of the disk unaccessible under normal conditions. If you ever do want to access this Restore Disk, simply hold down the option key while your Mac is booting up, and you should see be able to select it.
Time Machine, as far as I can tell, DOES backup system files. It full copy of your drive. Nonetheless, time machine backups are not bootable. You can save space by excluding system files, or any other big files you might not want/need to back up. Here are some articles that might help you with that: Time Machine tips and troubleshooting, Guide To Excluding Data from Time Machine Backups.
If you don't, time machine will leave them, no matter how old the data gets, and it would display an error/warning if you run out of space rather than deleting them. Time machine makes sure to always have at least a single full copy of your system.
Regarding space, you can backup a larger drive with a smaller one, as long as your Time Machine Drive can hold all the space you are using on your larger drive. So if you have 800GB in your system, but have only used 200GB, you could back it up with a 500GB drive, though it is not recommended, because if one day you do fill the drive Time Machine wouldn't be able to have a single full backup. Nonetheless, if you keep your actual disk usage below your Time Machine Disk capacity, you should be fine, with at least one full backup.
My final recommendation is you check those articles and save space for your backup, excluding the system files (Time Machine backups aren't bootable anyways. You'd need an installation disk or a Recovery Drive.) and any other large, unimportant files. Finally, keep an eye on your backup, and if you find out you do need more space I really recommend buying a larger hard drive! Time Machine can come up pretty handy in times of despair!
Best Answer
Yes, depending on the options you select when doing the migration.
In terms of documents and other data this will usually be fine. I'll provide an example below of when documents/data may be a problem.
In terms of software, this will depend on its compatibility with the version of MacOS you're running. For example, if you're running XYZ software that is only compatible with macOS Sierra and then restore that to a Mac running El Capitan, it will be copied across but won't run. Another potential issue is that you may need to re-register some 3rd party software (but if so, this is a minor inconvenience and does not result in any increased expense).
Now for my example of when data may be an issue. Your data will be copied across fine, but if the data is from a newer version of software that has actually changed the format of its data, then accessing that data from an older version of the software may be a problem. In any case, the data will still be there and is backed up.
On a final note, you would normally ensure the other Mac has an OS already installed when you restore your applications, documents etc.