What would happen if I don’t replace worn drivetrain components?
In my experience - breakage is not directly correlated to wear.  I've had bikes with unknown mileage on them, and have chosen to ride the transmission into the ground.
Generally the performance slowly deteriorates, with chain slip under power being a sign that things are getting bad.
Unlike other answerers, I've never had a worn transmission break and strand me or injure me.  The only time I snapped a chain is because I didn't reconnect it properly, and that one was perhaps half-worn.  I have twice wiped a derailleur with the rear wheel's spokes, but again that was misadjustment, not wear.
If you can afford to, replacing parts often helps maintain things in top-top shape, but for those of us with real world demands on our wallets, you can go quite far into the worn stage before it gets too much.  After all - you own it.
I find that climbs and going up grades are the most taking on the transmission and drivetrain so if its going to slip, its then, or when doing high power efforts like taking off from the lights.