It’s not as black and white as yes or no, some desktops will be slower than your laptop but cost wise a desktop equivalent would typically be faster, have more storage, etc.
With that said if the company doesn’t value time saved with a faster machine than you can help your workflow out by transcoding footage to formats like ProRes that are more forgiving to the editing process. “Proxy” files are typically some sort of intermediate codec like ProRes combined with a reduction in resolution / bitrate. This makes it easier for the computer to edit.
Most software will be able to use the original files or the original high quality transcoded files for export. Try to save these tasks for overnight or lunch when you don’t use the computer for anything else. Restart often, close other apps, and document your export times to justify a new computer ; )