Does sciatica contribute to or cause incontinence?

No: No but they may be related.

Not sciatica but the: Sciatica is caused by a nerve compression or irritation resulting in pain radiating down the leg. If nerves that supply the bladder and bowels are compressed as well which occurs in 1% of disc herniations, then this can lead to urinary retention and when the bladder becomes overfilled, then some incontinence may occur. This is a true surgical emergency that needs to be addressed immediately

Possibly: If sciatica is causing incontinence, you need this evaluated as it could suggest a more severe compression of nerves. if this does not resolve soon, see a spine evaluation .