Wave Solder an Alkaline Battery on a PCB (any concerns)?
I guess you shown us a lithium because you failed to find the equivalent photo with an alkaline battery. Actually, I doubt you can find pre-made alkaline batteries with the terminals as shown. So if your concern is manufacturability, that's something to check first.

Moreover, in case your circuit is mainly SMT with only the alkaline battery being through hole, I think it is worth it to ask the factory which solution is more expensive: reflow+manual soldering of the alkaline, or wave soldering with SMT+TH. I'm not sure the second is the cheapest.

Actually, I think the chapest and safest way to address this problem is to


choose standard SMT contacts for the batteries (e.g. Keystone makes some)
manufacture the whole board including contacts with standard pick-n-place + reflow process (without the battery of course)
have, during the assembly (I guess there is an enclosure anyway), a step to insert standard AA battery


Moreover, if you need to change the battery at some point, it's a lot easier.