Yes you have to upgrade the HMC(s) before doing the managed system's firmware upgrade.
Once one HMC is upgraded you should be able to do the firmware update but why wouldn't you want to upgrade the 2nd HMC? Going to V7R3.4 SP2 isn't very difficult if I remember correctly.
hmc firmware upgrades are downwards compatible but NOT upwards compatible. If you upgrade only one hmc and than the frame, you will have problems afterwards with the other hmc - if you upgrade both hmcs first, you won't have any issues and your not-upgraded frames won't have issues either.