Absolutely.

This is what happened to my E320. Cold starts were perfect. But after
being driven and standing for say 30 min to 4 hours it had a delayed hot
start - crank crank crank etc. And then started with a stench of
unburned fuel.

I found one spark plug was wet with fuel - that was the cylinder with
the "bad" injector. As the car had done only 37K miles I had only that
injector replaced. Its perfect now, after the repair.

Fuel injectors can be ultrasonically cleaned of fuel deposits and tested
by specialized shops, but a leaker due to a bit of rust inside must be
replaced. A Google search for "fuel injector service" should find a shop
in your area.

I replaced the fuel injectors on my 1987 300E a month or so ago.  Easy
two hour job.  The air cleaner housing and some rubber hoses must be
removed to get to the center ones though. Takes a couple of end wrenches
to unscrew the fuel line from the top of the injector, unbolt the
securing bracket with an allen wrench (then climb under the car to find
the little allen bolt you will drop!), pull the old injector out with
just your fingers, slip the new one in and screw the securing bracket
back down, then reattach the fuel line and snug the bolt.  By injector
number 5 and 6 it will take less than 5 minutes each.  Fire it up and
check for leaks.  You shouldn't need to bleed the CIS System to get it
to start.  Just cycle the flapper plate with your hand with the ignition
on if you have trouble getting it to start.

I ordered injectors from Performance Products.  Real Bosch injectors in
original Bosch boxes.  My early 300E didn't need the six rubber o-ring
seals they sell with them.