If I assign a specific race number to a constituent, like with a registration upload, will that number be skipped over in the normal registration process for that participation type, or could it possibly be assigned to another registrant as well?
There is no check when assigning race numbers to prevent duplicates. If you manually assign a participant a particular race number that number will not be skipped over in normal sequencing. Also, if you change the "Start Generating Numbers From" parameter, duplicate race numbers could be assigned. So for example, say I register person A and they are assigned race number 1 and then I register person B and they are assigned race number 2. Then I do a registration upload and assign person A to have race number 3 instead. When person C registers, they will be assigned race number 3 as well because it is next in the sequencing.
Keep in mind this is based on the individual participation type, each type will have it's own number list. If numbers are not staggered it will likely result in duplicate race numbers. For example, Participant Type A and Participant Type B can both have the race number 1.
For more information on how to assign race numbers to registrants in a TeamRaiser, please refer to this solution.