Can I use a transistor like a fuse?
Of course you can use a transistor as a fuse. I once built such a circuit for a low power AC/DC supply (I can not show you the full circuit, but you should get the idea):



Here's how it works: The sense resistor (R16) turns on a transistor (Q6) when the supply return current through R16 is > 0.5A. Then the shutdown signal (SHDN*) is set low and can be used to switch off the load with another transistor (not shown here). 

Ok, I admit that this circuit needs at least 2 transistors to replace the fuse. So this circuit shown here is only an overcurrent detector. 

The time constants (defined by R15/C19 &amp; R9/C18 in the circuit) will define how long the circuit is switched off before it turns on again.