Driving IRF540N with darlington
A 100 ohm resistor has a CR time of 180 ns when charging a 1.8 nF capacitor (the gate). 5 CR gets you easily to within about 99% of fully charged hence your rise time will be about 0.9 us.

I'd be a little concerned about the ULN2003A not properly turning the MOSFET off. According to the data sheet it will get down to about 1 volt with a 100 mA load and some MOSFETs might still be partially turned on even with 1 volt on the gate. I think you'll be OK with the IRF540 though.

If in doubt, you can always try the TPIC2701. It has 7 outputs and the same pin-out as the ULN200x but, importantly, the output switches on to near 0V because it uses a MOSFET with 0.5 ohms on resistance: -



In some applications you may not even need to use the IRF540.