Question
Are there any benefits/relief from chronic abdominal pain caused by crohns disease from the use of a TENS machine?

Answer
Dear Madeline,

There is some evidence that any pain can be reduced by TENS thus improving the quality of life: lots of people experienced more or less relief. Of course, TENS does not address the disease itself but only soothes the pain sensation, for example in the case of chronic pelvic pain syndrome. There's current research  showing that Transcutaneous Magnetic Stimulation can be more efficient.

You might also consider a mechanical tactile stimulation (MTS) showed to be efficient while having no adverse effects reported for TENS: while 12.5 % was cured and 43.8 % was improved, 1 6.3 % was worse after PTNS. Please take a look at ASHA Therapy. I personally know of quite a few Crohn disease sufferers using MTS for over decade.

Sources:
Schneider, M. P., Tellenbach, M., Mordasini, L., Thalmann, G. N., & Kessler, T. M. (2013). Refractory chronic pelvic pain syndrome in men: can transcutaneous electrical nerve stimulation help?. BJU international, 112(2), E159-E163.

Leung, A., Fallah, A., & Shukla, S. (2014). Transcutaneous Magnetic Stimulation (tMS) in Alleviating Post‐Traumatic Peripheral Neuropathic Pain States: A Case Series. Pain Medicine.

Hohmann C, Ullrich I, Lauche R, Choi KE, Rolke R, Cramer H, Saha FJ, Rampp T, Michalsen A, Langhorst J, Dobos G, Musial F.. The benefit of a mechanical needle stimulation pad in patients with chronic neck and lower back pain: two randomized controlled pilot studies. Evid Based Complement Alternat Med. 2012;2012:753583. Epub 2012 Sep 11.