Hate to be the bearer of bad news but the rule reads must be signed by June 1st to be kept.
Players drafted in the Major League Draft, who do not break camp (on Opening Day roster) with their MLB teams are returned to the FA pool. Players who were in an owner’s 13 keepers may be sent to the minors, although room must be made for them. Any player remaining unsigned on Opening Day remains on the owner's roster gaining zero points, but must be signed by June 1 to be kept.