Gear Torque

Attach a lever of known length with a small container at the end of it into which you can add weights (sand, grains of rice or something similar).
Add weight until the mechanism stalls and can no longer turn.
Multiply the weight by the length and you have the stall torque.
Measure the weight and length is suitable units to give kg metres. gram centimeters ounce inches or whatever unit takes your fancy (foot/pounds is what I relate too, but you won't get many of them from a clock).

Del

You could use a spring:

F = k Δx

First step is to find the spring's constant, k [Units N/m]. Use known weights of different weights to stretch the spring at least 10 different times. For each instance, measure the displacement Δx. Divide each weight [N] by the corresponding Δx [m]. Do the average and you have your k.

Next set up as follows:

Let τ = F y

Where F = k Δx

Then τ = k Δx y

Since:

k is known

Δx is measured

y is measured

Solve for τ

Hope this helps!!

Sure, there is probably some really complicated theoretical way of simulating it or calculating the wrong answer... but you'd need to know the torque generated by the prime mover.
You can't just start with a sack full of unknowns and expect to pluck an answer out of thin air. Maths isn't a panacea for all ills.

Regarding the 'will it slow it down' question, I'd think the escapement will either work or not work, and that will keep time... dunno though as it's not my field of expertise.
If you really want to know, measure it!!!!.

If you can't attach a lever, stick a thread onto the shaft with a spot of superglue and see how much weight it can lift, that's gotta be quicker, easier and more accurate than any amount of calculation.
Alternatively you could purchase the KrisDelTM book of random answers, which be about as much use as a calculation.
Del