Before producing I played guitar for about four years. Playing the guitar for four years didn't necessarily make me a better producer but what it DID do was it trained my ears and gave me a solid foundation of common chords, arpeggios, and scales. This combined with the religious study of music theory makes it easy to hear music very logically in numbers. Coming up with interesting lead solos is also a pretty fluid process since it's easy to think of what a guitar player would do.
After I started producing I eventually learned to play drums, bass, vocals, piano and how to DJ. Learning the piano was incredibly beneficial because it made it easier to sketch out interesting chord progressions. Meanwhile learning the bass to me seemed to be the least beneficial since for the most part it just follows the root of the chord. This is of course a huge generalization and can be expanded on if you decide to start incorporating lots of inversions into your music. I can easily see how learning the bass can help a producer learn how to make their baselines much more melodic instead of using static root notes. Playing drums on the other hand can help you learn how to program more realistic sounding grooves due to the amount of detail that you pay attention to when it comes to the dynamics of things such as the hi hat. Also, learning drum fills are pretty useful when it comes to transitions in between sections. Vocals were also incredibly beneficial when it comes to communicating with other vocalists and coaching them during the recording process. You begin to discover that there lots of different ways to sing the same word in regards to vowel pronunciation and vocal timbre. You can sing a word in a breathy tone, distorted tone, belted tone, or even using your head voice. Finally learning how to DJ is one of the best things you can do if you're trying to improve your arrangements. When you learn how to DJ you learn to analyze song sections and blend them between two tracks in a way that sounds pleasing. You begin to get a feel for the energy of tracks and the effect that adding/removing certain musical elements have on the dance floor. You also start to learn that after so many bars theres almost always an element that is either added or removed.
Do instruments help you become a better producer?
Yes. Only to a certain extent however. Learning an instrument will make you a better composer due to the nature of dealing with pure notes. Especially when it comes to the piano and guitar as a result of the polyphonic nature of these instruments. Learning guitar gives you a solid foundation on different types of phrasings such as staccato, legato, bends, slides and etc... This comes in handy when you're programming any type of lead sound. If you can get the notes to sound good on a piano or guitar then chances are they will sound good when you transfer the arrangement to EDM or whatever genre you're making.
What learning an instrument will NOT help you do is become a better audio engineer. It will not help you become a better electronic music arranger (with the exception of learning to DJ) since the sounds used in electronic music are generally synthesizers and not acoustic instruments. It will not help you when it comes to learning how to make the PHAT n DIRTY bass sound in your favorite track. It will especially not help you when it comes to making music that is more focused on sound design like dubstep.
Bottom line... if you wanna improve the MUSIC side of your composing then learning an instrument is a great idea. If you're looking to improve the technicalities of your productions (sound design, mixing, mastering, arrangement) you should look elsewhere.
