Legal, yes. Against management's policy, yes. Search prior to entry possible, yes.
You should feel safe, though, after all their policy is for the safety of all guests.Weapons
For the safety of all guests, weapons will not be permitted in Safeco Field. The only exception to this is law enforcement personnel in the performance of their official duties. The presenter of a game ticket consents to a reasonable search for weapons before entering. Failure to comply with the above conditions will result in no admittance or ejection.