Yes, there must be a link between them so that the two devices may send HSRP hellos (multicast traffic to destination 224.0.0.2 on udp port 1985) between them, and also so that it can route your traffic. The link can be a trunk, etherchannel, or a single vlan link. As long as traffic from the subnet that HSRP runs on is able to cross the link, you are fine. Etherchannel increases stability in case the single link fails though. It doesn't have to be vlan 1, it can be any vlan number that the HSRP group subnet is on.
Hope that helps.
Steve