Is distortion okay?

Only if you intend it to sound distorted.

Let it be known that loud sounds alter the hearing process and cause distortion in the ears. You’re not hearing a loud sound exactly as it really is. Your ear is actually changing that sound in order to protect itself.

Slight amounts of distortion can add fatness to thin-sounding signals. Most equalizers induce varying amounts of distortion. Especially cheap ones.

Of course you wouldn’t normally introduce enough distortion to make it audible and obnoxious, unless the music requires it.

Big, powerful solid-state bass amplifiers are built to deliver a pure clean sound. When recorded, this can sound thin. There have been studio session bass players that use an alternative amp for this purpose. It would be low in power, use tubes instead of transistors, and therefore distorts when cranked up.

Similarly an amp’s loudspeakers may be perfect for stage but might sound thin in the studio. Today’s speakers are very clean at high sound levels which doesn’t always produce a heavy sound on recording.

Try using some older speakers and overdriving them a bit. This usually produces a slightly distorted but fatter sound.

Distortion from foot pedals for electric guitars are the most common form on intended distortion. Commonly known as “fuzz boxes” they have been used on countless recordings since the sixties.