No. Unless specifically stated otherwise through agreement by all rightsholders, all licenses on Songtradr are non-exclusive. This means that songs can be licensed multiple times for multiple uses by different buyers.
There are rare instances of exclusive licensing via Songtradr. If a buyer wants exclusivity for a certain type of use or territory, a Songtradr representative will work with the rightsholders to negotiate an appropriate price for an exclusive license, which will most likely be higher than the price for a non-exclusive license.