Interesting question.
Deaf people vary in the amount of hearing they have and therefore in how much they may actually hear when listening to music. It will also depend on the setting where they may be listening, concert hall etc. Some venues have what is called a loop system that directs the music or singing directly into their hearing aids to enhance their listening to the extent they may have some hearing experience with hearing aids or cochlear implants etc.
Further, the extent to which an individual may be able to pick up on a singer being "off key" will vary and the knowledge an individual deaf person may have about music, singing etc will vary depending on their experience, background, interests etc.
If interpreting in a setting where you don't really have access to these variables and wanting to convey that the singer is "off key" or as you say "tuneless" you would need to use a technique referred to as expansion which is basically like an explanation of a concept after starting with some general signs explaining what is occurring. For example, suppose the audience in general is reacting to the sound being "off key" as an interpreter you would need to explain the audience reaction. For example, SINGER "OFF KEY" MEANS VOICE NOT MATCH SOUND MUSIC. AUDIENCE NOT ENJOY SINGER VOICE. SINGING CONFLICT MUSIC.
Something like the above would be an expansion that is an attempt to explain what is happening. It may be impossible to truly explain what being "off key" is. If there was time to further elaborate you could explain something like MUSIC FLOWING-UP-AT-THIS-LEVEL, SINGER HER VOICE NOT MATCH, SINGER VOICE FLOWING-AT-THIS-LOWER-LEVEL. THESE-TWO NOT MATCH THAT O-F-F K-E-Y.
This is how I would handle this situation if I were interpreting but it will be very context dependent. There is no direct way to communicate what "tuneless" means. Maybe placing your finger in your ear and wiggling it up and down while shaking your head in exasperation like it is hurting to listen to this would be a short cut way to say something is not pleasant to your ear about the singing but this won't tell the deaf person necessarily what this experience is actually like.
Let me know if you have additional questions
