The server will not remove an object while it is being accessed. For example, if a trove operation is in progress reading data from a datafile, the server will queue a subsequent remove operation on that object until the read operation completes.
The server is free to return ``no such file'' results to future operations on that object even if it has not completed the remove operation (assuming that permission checking has been performed to verify that the remove will occur) or to queue these operations until the remove has occurred, then allow them to fail. Obviously the first of these options is preferable.