Matching the your game's theme, feel, graphics, and audio all together is a great thing to do because each one will strengthen the 'messaging' of the others, and it also increases immersion and raises the bar of willing suspension of disbelief.
So from a general perspective - YES! If you decided on a retro feel and a retro look, then add a retro sound in, as well.
With that being said, don't let the limitations of yesterday's technology limit you. Just because a certain sound couldn't be done using retro SNES-level technology doesn't mean you can't have it in your SNES-inspired game. Your music doesn't need to actually SOUND like it came from that era; it only needs to FEEL like it sounds like it came from that era.
As a visual example, here's an in-progress version of Equip screen in a game that's inspired by old-school retro games (the character portrait and the item icons are placeholders; the final portraits will have a pixelated look in the same style as the background):
As you can see we've tried hard to replicate the feel of an old Tube TV with the framing, the "low-res" staticky background, and the very blocky text. But the background is actually a high-res PNG, the text has anti-aliasing to make it a little easier to read, and some of the UI elements were made with a clean look so as to keep the screen visually pleasing and impressive, despite its very low-tech theming. Old-school menus were ugly and difficult due to technological necessity (e.g. 240x240 pixel resolutions); a new game's menu inspired by the old-school ones should capture the same feel but it shouldn't be ugly nor difficult because it doesn't have to be.
Taking the same concept to sound and music - don't rely on MIDI instrumentation, but instead use sounds that feel like they'd be at home in a MIDI environment, and even layer a few other sounds and instruments (electric guitars tend to work well) on top of those sounds if it helps sell the mood of a scene or level! Chiptunes are fine, but so are full, modern-tech compositions that use a lot of boops, bleeps, synths and sinewaves.
If you're looking for such music already made, I highly recommend
Incompetech, which is an impressive collection of commercially royalty-free music (credit required). He has dozens of loops that, despite being fully modern in their quality, have a feel that fully reminds you of old-school video games. From the page that I linked, choose the genre "Electronica" in the search fields, and most of those songs will be in the style that I'm describing.
