After exporting from InDesign to PDF everything looks in place, while InDesign shows a lot of links missing. I am wondering if it could be printed without problems?
If the links were broken upon export, what was actually exported were the low resolution preview images.
In most cases no. They generally can NOT be "printed without problems"..
You can preflight the PDF to check the objects and see that their resolution is probably pretty low and unacceptable.