I have a DNA fragment that contains the gene of interest sandwiched by restriction enzyme sites. Then, can PCR amplify the entire fragment, recognizing the restriction enzyme sites?
If you aren't digesting prior to amplification, sure. Nothing in PCR cares about whether or not some other protein interacts with the site. There are thousands of restriction enzymes in nature. No one would ever be able to do PCR if you had to avoid every single potential restriction site.