Good question... I think so

Based on the total kills weekly challenge, the totals used were taken directly from the kills stat total for all participants.

With this knowledge, it would stand to reason the tabulation of assists would be the same.

So in short, yes assists that are achieved via using the recon drone will count because they get added to your overall assists total.

The only "assists" that will not be counted are from holding the flag in team defender because these assists do not get tabulated in your overall assists stats total.