Depends on if you want arpeggios to run. Envelope followers and drum kits do not require ARPs to be running - but you may want ARPs on if you are wanting any arpeggios to run. There's not quite enough information to guide you either way here.

When using the envelope follower with a drum kit, does the ARP ON/OFF butto, need to be kept ON?

No. The ARP ON/OFF button only needs to be set ON when you want an assigned Arpeggiator to “play” the drum kit. If you wish to “play” the kit manually, you can.

There are two ARP ON/OFF switches you need to be concerned with: the Main Arp On/Off and the individual Part Arp On/Off Switch. They must both be active in order for the assigned Arp Phrase to “play” the Kit... additionally you must press a Key within the specified Note Range and Velocity Range to initiate playback... then and only then will the Arp Phrase play. Arps can be set to Loop or play once.

If you would like to “play” the Drum Kit manually, make sure the parameter ARP PLAY ONLY is set to Off.