Seven months with zero replies through the contact form is not normal even for them, but it doesn't necessarily mean anything bad happened to your order. In my expirience the contact form emails go into a black hole when they're slammed. Calling is what actualy works. I ordered a kit and some electronics during a sale a couple years back and heard nothing for about ten weeks. Two form emails, nothing. Then I called the shop number during business hours and had a real conversation with someone who pulled up my order on the spot and told me exactly what was waiting on what. Box showed up less than three weeks later. The thing to understand is that most of the delay on sale orders comes down to motors. There's been a serious backlog on hobby motors for a while now, and if your order included any, they might literally be sitting in a queue waiting on a shipment from the manufacturer. The kits and bays they can build in house, so those parts are usually ready much sooner. Ask them if they'll split the shipment and send what they have now. They've done that for me before without any fuss.
To answer your other question directly: no, the box does not just show up one day with no warning if you've been in contact, but if you've been silent for months then yeah, it can absolutely appear out of nowhere. I've had orders land on the porch that I'd half forgotten about. On the card dispute, I'd hold off for now. Disputes are usually only good for a limited window after the charge anyway, and at seven months you may be past or close to the cutoff depending on your card issuer. More importantly, if the stuff actually exists and is just stuck in a backlog, a chargeback gets your money back once and guarantees you never deal with them again. Call first. If you get a real person and a real answer, keep waiting. If the phone goes unanswered after a few tries across a couple weeks, then start thinking about the dispute route.