Printing an Illustrator file that contains raster images with transparency?

Question

I have an Illustrator CC file with some embedded PSD files. Some of these have a transparent background, while some have the same kind of background and opacity set to 50%. I have some vectors too with opacity set to less than 100%. Will this print correctly?

All elements and the file itself are set to CMYK, all text converted to outlines, have a bleed area, all PSD files are embedded to the file. Have no spot colors.

I'm not able to try different variations and go to print shop several times (if something doesn't work), so I'm asking here if the file as it is is able to be printed without glitches.

I've been looking for an answer to this question online (here too), but seems like I can't find a solid answer (or maybe don't understand answers I read).

Answer 1

Apart form PDF for print export the picture as jpg. If the outcome will look like the one you want then send that preview file for printer as a "proof" of what you want to have on final print.
If the printer will be unable to do so with provided pdf they should tell/write what to do within the file to have it on their machines.

Answer 2

So, if someone has the same question:
Transparency will print correctly if the "flatten transparency" option is applied to a file.
I used PDF filetype. I selected all objects of the artwork and applied the "flatten transparency", with all other options set as in my question.

Thank you all for your effort, you helped a lot.