For a double replacement reaction to occur, is it that one of the products must be insoluble and form a solid?

There has to be some mechanism to remove the products from the reaction so that the reaction does not proceed in the reverse direction. Product needs to be removed: solidification, removal as a gas are common methods that in nature this is occurs.

So is the answer to my question yes?

Yes, for a double replacement reaction to occur, one of the products must be insoluble and form a solid. This is because in a double replacement reaction, the cations and anions of two compounds switch places to form new combinations. If one of the products is insoluble and forms a solid, it can be easily separated from the reaction mixture, which helps drive the reaction forward and prevents it from proceeding in the reverse direction. Solidification or removal as a gas are common methods used to remove the product from the reaction.