Conroy went to hospital after the match where it was discovered that he had in fact broken two fingers.
A three-week lay-off for Conroy has put Boston on red alert for a goalkeeper as United look to stay out of relegation trouble.
Meanwhile, Pilgrims boss Neil Thompson has admitted he is keen to extend Paddy McCarthy's loan spell at York Street.
"His third month is up in two weeks. He's enjoying it here and playing well for us," Thompson told the club website.
"We can't take him on loan for any longer but I'll be trying to speak to Manchester City soon."
