If we are planning to publish thousands of pages. Does it make any difference to publish them with Normal or High priority (assuming no other publications are going on)?
If these are the only jobs in the queue, then it won't make a difference. The priority only influences the order in which the jobs are picked up from the queue, not how fast the publisher/transport/deployer will do the work - this is always "as fast as possible" independently of the priority.
As Nuno said, it only really affects the order, however if you have the possibility of multiple publishing servers, you can nuance it a bit. You can configure a publisher to only service specific priorities. Usually this would mean a server dedicated to high priority jobs.
Of course, high priority jobs will get picked up first, but only once the items currently being processed are finished. So if you have a very big publish transaction that isn't high priority, it could still block a high priority job until it finishes. Having a separate publisher for high priority jobs can alleviate this.
Even with only one publisher, understanding how it works helps. So knowing that high priority doesn't make it go faster, your logical choice for your bulk publish action is to do it at low priority. Then other jobs can easily be given higher priorities if needed.
And of course, if you really do need to make it go faster, you might want to look into how quickly you could provision an extra publisher server.