I have completed a campaign with SWMT and gotten missing VO throughout, soldiers and officers alike. The soldiers' kill taunt VOs going AWOL was tracked down by BlueRaja as a side-effect of one version of SWMT (the audio pipeline depends on one particular pause, it turns out). This has been fixed by BlueRaja. The rest of the trouble is a feature of XCOM 2.

After the missing VO problem, I started a sister campaign without SWMT (cosmetic mods only, i.e. camo patterns, CapnBubs Accessories Pack, that's it). I still got missing VO, it just felt like it took longer for it to appear... but that is probably because combat and Avenger movement was that much more tedious, i.e. it took a much longer time for each action and battle to play out.

It seems to me that XCOM 2 corrupts its VO settings or output over time. Your mileage may vary. I can restore VO temporarily by loading a save, any save, but it goes away quickly again. The only long-term fix for me is to verify Steam's local files, then the VOs stay for a while again.

PS. In light of some reports, please check your audio settings too: you can opt out of many VO lines if you don't tick the right boxes.