Once you are under contract, the LA must update the status of the property in the MLS and this change from "active" will alert other agents that it is under contract and whether or not there is a kickout clause. Non agents searching the various available websites that get their data from the MLS will not see that status change. The property will just not show as being active and will generally not show up in their search for properties.
That being said, if there is an offer and you accept it (putting your home under contract with a contingency and a kick out), the agent will put it in the MLS as contingent with a kick out. The listing will no longer be active, and other possible buyers would have to search the listings under contract and contingent to find your listing. In this case, they already know you have a contract and that it is contingent with a kick out.
Yes, sellers/listing agents are required to change the status of the listing to "CONTRACT/KICK OUT" when such an offer has been accepted. This notifies potential buyers that there IS an offer already on the table but also that the seller is continuing to market the property until the "contingency" is satisfied by the current buyer or expires. In the event another offer comes in without a contingency, the seller must give the buyer with the contingent contract an opportunity to waive their contingency & move forward with the purchase prior to accepting the non-contingent offer. In the event the contingent buyer cannot waive their contingency & move foward with the sale, the seller can then accept the non-contingent offer.