High current, slow turn-on, low ripple power supply
Yes it most likely work.
It doesn't make much difference in linear power supplies because you don't have much of ripple at the input. tantalum capacitors usually used for switching power supplies, where ESR matters.
The resistor on the emitter is to match the transistors. it's called fixed bias which you can read more about in here. and for this design you don't need it.


As a hobbyist who is also in the process of building a power supply based on LM317, I'll share some of my experiences:



Lab PSU, PCB design

If you are going to draw more than 1 A from the supply and as you mentioned for cam which is going to run 24/7, using linear power supply is really wasting energy and money.

I suggest that you use a switching power supply with high frequency and design a filter for it's output to reduce the ripple to minimum. and that is going to be another question.



Edit:

If you want to draw only few mA, you can simplify your circuit and remove the bypass transistor. LM317 can provide up to 1.5 A, just make sure it's installed on a proper heatsink.