Short answer: yes — but only in a limited way.
With Suno, you can keep your voice and add instrumental music, if your voice is already part of the uploaded audio.
How it works in Suno
Suno lets you upload an audio file (for example: your vocal recording).
It will then generate music around it (instrumental + arrangement).
Your voice stays, and Suno builds the backing track.
Important limitations (this part matters)

Suno cannot remove vocals from a mixed track.

You cannot upload a vocal and ask for “instrumental only, no vocals added” in a precise studio sense.

You cannot fine-control instrumentation (like “only piano and bass, no pads”).
Best practice (recommended workflow)
Record your voice clean (no background music).
Upload that file to Suno.
Prompt something like:
“Add gentle instrumental accompaniment. Do not add new vocals. Keep the original voice intact.”
This usually works pretty well, especially for:
spoken word
chanting
simple singing
nigun / recitative-style vocals (which I know you work with)
If you want full control (alternative)
If you want:
exact tempo
exact instruments
zero AI vocal interpretation
Then Suno is not ideal. In that case:
Generate an instrumental-only track in Suno
Then combine it with your voice in:
Audacity (free)
Reaper
GarageBand
Logic / Ableton
If you want, tell me:
spoken word or singing?
style (ambient, nigun, cinematic, folk)?
already recorded or not yet?
I’ll tell you the cleanest way to do it for your use case.