Yes and no. Splatoon 2 does support voice chat, but only through the companion mobile app (which is yet to be released). You can use said app to organise lobby times with your friends, and communicate with them on it as well. You won't be able to communicate with strangers (their used term, those who aren't added as friends, and I believe it can't be used in public Turf and Ranked matches either [will most likely support squads should they return]). In Private you can communicate with all 7 friends in the lobby until the match starts, where you can only speak to and hear your teammates during the match.
SplatoonJP and SplatoonUS highlighted those features a few months back, and you can read the English version here if you desire:
https://splatoonus.tumblr.com/post/156676664164/weve-received-a-report-that-splatoon-2-will-be