Could it lead to a blown motor?

 

Theoretically possible but highly unlikely.

When the exhaust valves especially are restricted over time with the "pounding shut" action of the valves, the engine doesn't breathe as well because exhaust fumes are not fully released. The engine will not run as well without proper exhaust venting, but it will still run.

So over time, you could theoretically burn out an engine the more the exhaust becomes restricted. But it would take a long, long time to get there, and something catastrophic unrelated to exhaust venting would probably take place first.

There are probably thousands of high mileage Fits out there that haven't ever had a valve adjust. They'll still run, but mileage and performance will suffer, and these little Fit engines aren't exactly known for gobs of power - every little bit helps.

 

Although, I don't specifically know what valve system the FIT has, I do have several motorcycles with solid lifters (no auto adjustment takes place). As the miles add up, the valve beats itself against the seat and both get "thinner" over time. That allows the valve to travel up towards the overhead cam and close the original gap between its stem end and the cam lobe = getting tighter.

If the gap disappears altogether, the valve doesn't seat / close completely and the super-hot gasses of combustion will behind to flow between the valve and its seat. This starts to cut into the valve and seat to the point it can't be repaired - all needs replaced at additional costs.

On my bikes, if the valves are too quiet, I have problems - burned valves / seats. If they are getting louder, I have a different problem - the adjust screw / locknut has worked loose (old BMW) or I'm getting excessive carbon build up on the valve / seat and the valve stem to cam lobe gap is increasing (newer Kawasaki that uses shims).