The two processes you cite are very different and are unlikely to be interchangeable.
Proteins are transported into the endoplasmic reticulum while they are being synthesized. This process is called cotranslational translocation. This was discovered by Dennis Sheilds and Gunther Bloebel, who received a Nobel prize for the work. See linked Wikipedia page below.
https://en.wikipedia.org/wiki/Protein_targeting
I knew Dennis Sheilds when he was at Albert Einstein College of Medicine.
Fully synthesized proteins are transported into (and out of) the nucleus via the action of nuclear transporter proteins (importins and exportins) that require the activity of the GTPase Ran. Here is the link to the Wikipedia page on that process -