I think the vampire physically could enter because the warrant is basically allowing them to enter a space they otherwise would need express permission from the person that dwells there. I haven't known a cop otherwise to serve the warrant and then just stand awkwardly waiting for permission to enter afterwards. If we are to believe that vampires exist in this context and follow "traditional" rules, you best believe a vampire could be in any given profession, especially because night work is more prevalent than ever. There would certainly be a vampire cop who works at night and takes advantage of the way warrants work.