Chrisdm, to better answer answer your question, no you should not attempt to run this dropin off primary cells (in any configuration.) The current draw (amps) is way too high and the batteries cannot handle the load. Also, the dropin itself has a maximum input voltage rating... If you put 2 CR123's together end to end (this is called "in series") you now have 6V instead of 3V. If you put 3 CR123's together in series, you get 9V.
This would be way more volts than what the dropin is rated for.
To get past the current draw and capacity issues this dropin presents, many people are running these off of a newer high capacity "26650" cell. These offer the voltage of a single Li-Ion cell, but with a little more capacity, and better max current draw ratings.
A popular 26650 host can be seen
HERE. (What I'm using.) Another benefit to using this host aside from it using a bigger battery, is that the host itself is bigger, providing even more heatsinking.
And a good battery choice to go along with this host is
THESE. (What I'm using also.)
EDIT: Chrisdm, also I see you have the 5.6 Amp version ordered... If you decide to run this on an 18650 setup, only use a
very high quality 18650. Your dropin will be pulling down between 5-6 amps on high, which is
ALOT. (This is nearing the max current draw limit of even the best 18650's.)
Cheap batteries do not like this much current draw and could "vent with flame." Which I am sure is not what you're after.
The 26650's that I posted the link to have a 10A normal discharge current rating, and a 20A max continous discharge rating,
much better for this application.