I use conscripts as protection for my heavy artillery and to fill in the gaps to quell resistors as my artillery and armor push forward. For example, if the Soviet AI is consistenly attacking with 10ish IS2's, I include 20ish conscript infantry with the artillery divisions. In a way it's served more to actually deter the AI from attacking rather than sucking up actual losses. If the AI sees it can't get to your 'easy' units, it tends to look for a different target elsewhere.
I have not built a single actual infantry unit in the entire scenario... There's simply no point. Regardless if it has 2 hp's or 4 hp's, any armor unit will kill my 6-8-1 infantry so why bother? I consider my true 'infantry' as the HMGers (3-14-1).
When I take over towns, immediately after building the typical Temple > Colleseum > Cathedral setup, I usually set the city to make me a few workers. What that does is bleed off some of the population so that when the city grows again, the growth are Argentine citizens which are draftable. You can't draft foreign citizens as far as I know so after a few workers pop out, the city will grow faster, thus supplying me with 'free' infantry. I have done a total of three 'nationwide' drafts in this scenario where I call on conscripts from every city that is eligible (that being population 7+ with at least one Argentine citizen). Typically I only do that when I am conquering cities faster than I can produce HMGs. I ALSO draft anytime a city reaches it's natural growth limit regardless of size. On larger cities, a draft won't take any production at all away from the city since, at most, a city will use 21 hexes and then make tax collectors, entertainers, and scientists.
Anyways, that's the basics I think.
Argentine Update:
Week 11, 1944:
The Soviet front has totally collapsed... We have linked up the European and middle eastern/African forces and can now move forces freely. We now control the line of Riga - Smolensk - Tula - Stalingrad - Grozny - Tehran... Our heavy artillery took one hex of the Moscow line down to one hp and an army came in and finished it off. The road to Moscow is now clear and Soviet counterattacks are down to 7 IS2's or so per turn. Our numbers now stand at 36% land and a whopping 61% of world population.
Here's a breakdown of our current armed forces... I apparently underestimated the amount of heavy artillery I had about 12 game weeks ago...
328 Conscript infantry
229 Tank divisons
405 Heavy Artillery
149 HMGs
10 Elite Tank Armies
57 Fighters
8 Recon/Bombers
47 Destroyers
34 Heavy Cruiser C2
6 Submarines
40 Tranports
Sheer weight of mass and production makes our victory almost assured at this point regardless of the civ AI's increasing tech advantage but I'll probably play it out just to finish things up.

I haven't seen any Allied advanced armor yet but I'm sure I will at some point as Britain is the largest civ left after the Soviets. I'll have to take at least some of their cities to reach 80% population probably.