Yes - infact the day the surrendered there were still boats arriving with arms and food stores. General Floyd actually escaped on one of the boats that had just arrived with fresh troops. Also, if you read about Camp Douglas in Chicago, the Confederate prisoners were free to walk about the city and infact is how some of them escaped. This changed overtime when a new Union command structure was in place at Douglas. But yes, Grant as was his staff, overwhelmed with the number of Confederates that they had just acquired (close to 15,000) and up to that point, there was no real process in place to handle it.

John Walsh