In general: NO
This is really bad UX: creating actions that affect other pages the user can't see and maybe don't remember is the definition of an anti-pattern. You'll always need to make sure that users are aware of the consequences of their actions, otherwise they'll need to re-do everything again, even if they didn't even try to do what they were forced to.
There are a few particular cases where I have seen this kind of bad behavior, most commonly e-commerce sites. However, they don't do this in order to provide good usability, but in order to maybe get more sales (so at checkout you'll need to delete the products you really didn't want or even marked days ago. As an example, GoDaddy did this for years)
If your case is an e-commerce one, just offer a cart option like everyone does: instead of checking a grid element, make them add to cart.
Similarly, even if this is NOT for an e-commerce site and you only want users to group items of interest, just offer the same "add to cart" functionality (obviously with another name) and then create a page where all these marked elements are grouped together