It is possible. You can try to wash out your ears in the shower, and that typically will clean out any debris from the ears. If you are really concerned, either visit your hearing aid dispenser, or the hospital and have them take out the wax guard.
You could also use a bulb syringe from an ear washing kit and flush out your ear. What is good about this method is you can use gravity in your favor by positioning your ear with the wax guard over the sink and flushing it out with the bulb syringe. Close the drain on the sink so you will know when you have removed the wax guard.
LOL!! Same thing happened to me a few years back. I removed one of my Oticon hard-shell aids and that little white wax guard was NOT on it, leaving a cavernous black hole in its wake. I optimistically thought maybe it’d dropped off on the carpet? Never found it … until about 6 mos later, I was looking in my ear sideways and … HOLY COW! Right there, perched in the doorway of my ear canal was the white wax guard. My hubs tried to snag it with tweezers, but gave up, so I had to go to my aud-guy, who was as mystified as me how that little wax guard had sat in my ear canal for MONTHS without any degradation in my aids or triggering an infection.
Some ENTs have TINY vacuum-cleaner pipes that they poke into the ear to clear out debris - I’ve had that done, too. You will get this thing out, just don’t panic (like I did), wondering what will happen.