Yes, all abilities that utilize the same system (all ranks of Torpedo: High Yield use the Torpedoes system, for example) have a 20 second global cooldown. At max rank you can use a THY ability every 30 seconds; with 2 of them, you can alternate them every 20 seconds. Up to you if it's worth it, but most people would say no.
Looks like you missed the double shot at 21 seconds. But if you spaced out your torpedo shots so you could use them exactly when THY was off cooldown, then you're only getting 1.5 additional torpedoes every 20 seconds on average (2 additional torps for High Yield II, 1 additional from High Yield I, alternating the ability every 20 seconds with a 1.5 average increase in torpedo number). Move up to a 60 second firing iteration, assuming you only fire torps when High Yield(s) are off cooldown, you'll fire 10 total torpedoes by mixing the 2 abilities (3 from HYT II at 0 seconds, 2 from HYT I at 20 seconds, 3 from HYT II at 40 seconds, 2 from HYT I at 60 seconds), or you'll fire 9 total torpedoes by just using HYT II (3 at 0 seconds, 3 more at 30 seconds, 3 more at 60 seconds).