Sure. Tho your car has an ECU, it is not an ECU switching the relay.
And it's a (mechanical) switch doing the switching, hence not
electronic as in ECU, computer, digital or analog circuit, etc.
However, tho there is no harm including such "spike suppression" diodes, many hereon claim to never have witnessed any damage by NOT including one - even when energised by ECUs etc.
I'd argue in your case it is optional but not necessary - ie, if it costs extra or adds inconvenience, forget it.
In some cases the spike might effect other circuits. I have seen LEDs or dash bulbs flicker in response to spikes on their supplies, and have read or heard of VERY RARE cases of damage - eg, a
remote light or horn relay blowing an ECU or radio etc. However I'd argue those cases involve sub-quality ECUs & amps etc.
The one thing I argue
against is relays with inbuilt spike protection diodes. IMO it is much better to supply the diode externally. You can therefore add your own or replace a blown diode, and do not have to worry about which end of the coil is +ve or -ve. [Hence the convention with (old style?) Bosch/Hella etc relays where 86 is coil +ve and 85 is coil -ve (GND). To connect those the other way for a relay with inbuilt spike diode means a short from +12V to GND thru the diode and that's not the sort of smoking session most people look forward to.]
Modern relays avoid such polarity issues. They use resistors etc instead of diodes, else make the designer/user mount the diode as part of the relay's wiring base or harness.
A bit more (optional FYI) detail...
The diode is there to prevent voltage spikes that could damage other electrics - eg, electronics.
The spike occurs when the the coil is de-energised - ie, you switch off the relay - IOW
open the coil circuit. The coil tries to continue its current flow and therefore generates a big voltage spike.
Such spikes are commonly up to 200V but almost always below 400V for 12V & 24V systems. Hence 1N4004 or 1N4007 diodes are typically specified for "spike quenching" of coils up to 500mA.
A "backwards connected" aka
reverse-biased diode conducts when the spike exceeds ~0.7V, hence "clamping" any (say) 400V spike to between 0.7V below GND (ie, -0.7V since GND = 0V = zero Volts) and 0.7V above the relevant +ve supply - eg, the +12V supply (which is usually 12.7V on a full battery and typically up to around 14.5V when driving/charging).
All
automotive 12V electrics should handle such a range.
In early electronic and digital car days, and more recently with cheap or pathetic designs, manufacturers may not have included suppression for spikes. However these days all +12V power inputs should handle (say) up to +16V steady-state, and spikes up to 400V etc.
Similarly any output that might be expected to drive a relay
should have inbuilt spike protection - ie, a $0.05c reverse biased diode ACROSS its output(s).
Having said that, I still see the occasional "modern" product that specify that YOU must add the diode if driving a relay. (Like wth did they expect us to be using - a MOSFET or solid-state relay?)
Sorry if the above got a bit much. In retrospect it's all so easy... Once you realise a diode can only conduct (
conventional current in the direction of its
circuit symbol arrowhead (... and that the line on a real diode is the same end as the circuit symbol ie -->|-- ie so current can only flow out of the line end; the line (or brick wall) stops current flowing
in from that end, you can begin to analyse and figure out your own use for diodes. (See the
Diodes link at the top of this page.)