If your receiver doesn’t have HDMI inputs you don’t need it. But you do need to connect an audio output from your TV (or source) to one of your receiver’s inputs to get audio.
HDMI carries both audio and video but you don’t need video to go from your TV to the receiver, only audio.
Whatever you are using as the audio source (TV, SAT box, DVD etc.) needs to be connected to one of your receiver’s inputs but doesn’t have to be via HDMI.
If the source doesn’t have RCA outputs and only HDMI or optical then you’ll need a separate converter box to go between the source and the receiver that will adapt the source’s output connection type to the receiver’s audio input connection type.
An ARC HDMI is ideal though because it will turn a receiver that has "ARC" HDMI inputs on and off automatically whenever is senses an audio signal from your source.