Hi Juan,
It can certainly be done but you may have some things going on that require special handing/attention to optimize your specific workflow.
The most straightforward way would be to render/save your assets out of Illustrator in a compatible image format and then open those images in OpenToonz.
Without knowing more specifically what you are trying to accomplish I'm not sure what more to suggest.
I'll take a stab at it though...
You mention props and backgrounds... simple enough.
What I would do is render/save out each element of your Illustrator file that you need to be manipulated separately.
You'll want a format that uses transparency/alpha channels such as PNG, TGA etc.
If you have a background that consists of only one level... that's an easy export/import from Illustrator to OT.
If you have multiple parts (mountains in the far distance, lake and/or house in the middle and trees in the foreground) you would save each part of these out with transparency (alpha channel) so that once in OT they can be manipulated separately.
The same would be true for a character (that you might want to animate in cut out fashion in OT).
Render/Save your character's body, head, arms, hands, legs, feet, eyes... whatever needs to move separately as a different image and them bring them all back together in OT.
If only one part of a character will move (such as the eyes on a face or a smile... or mouth shapes)... save everything out of Illustrator except those elements you want to animate/move and then either save those out separately for import or completely create/recreate them in OT.
I suppose the simple answer is just 'save out of illustrator into a format that can be brought into OpenToonz'.
Let us know how you fare and if you can provide more specifics we'll try to give you more specific feedback.
Good luck!