At least in one case. A 23-year-old woman, who lives in Manchester UK and works as a typist, wrote me:
I’ve recently been trying out a standing desk, partly due to reading the posts you made about them. For the past few weeks, I have been tending to stand instead of sit when at my laptop, normally for more than 3 hours a day. I sit down when I get bored of standing and I walk around lots.
I was looking out for mental clarity effects but I’ve not seen a clear effect in that direction. What I did find surprising, though, is that my chronic but mild IBS symptoms have abated. I get heartburn/acid reflux regularly, and gut cramping, but since standing more these have all but stopped. I think it’s because standing up puts less pressure on my stomach and gut and leaves them more opened up.
I asked how long she’d had the symptoms (heartburn/acid reflux, etc.):
I think the last 3-4 years, but it’s hard to say when. I think my IBS probably started happening when I started having problems with anxiety but I wasn’t keeping track back then. 
I’ve suffered from recurring depression for 10 years now, but severe anxiety for me is relatively new. I think it would make sense if it coincided with the anxiety – I’ve heard of Citalopram (an anti-anxiety medicine) also being prescribed in a low dose for IBS, and some of my friends who have taken Citalopram + who have had IBS have had it go away. I never actually got a diagnosis for IBS, but it seems a fair description. The symptoms are heartburn, gut cramping (sometimes very painful) and my stool being quite variable in solidity.
I asked how long had she been standing more than usual:
4 weeks, when I’ve been able to. At work I have to sit, often with bad posture, but the last two weeks I have been on holiday. When I stand, I notice an improvement on the same day that I’ve been standing more. Part of what motivated me to stand with using my computer was when I recently spent a day walking around Manchester (where I live). I noticed that my energy levels were much smoother even though I hadn’t eaten very much and that my gut and stomach felt more OK than usual.
I asked what other remedies she’d tried:
About a year after I started regularly getting heartburn, a friend told me about antacids, so I started taking them when I needed them, but they weren’t always effective and they don’t help with gut cramping. Peppermint tea worked to some extent but would give me strange headaches and made me feel bloated. Peppermint oil capsules were an improvement – no bloating but still giving me headaches. I’ve also tried various dietary changes. I find that dry carbs (like toast or potato crisps) tend to bring on or make worse heartburn and cramping so I sometimes avoid those. Also when I’m hungry I get heartburn quite badly, so I’ve tried to eat things that level out my blood sugar over time more (e.g. eating more fat and protein, fewer sugars and carbs). I tried probiotic soy yoghurt (I’m vegan) to see if that would help but it doesn’t agree with my stomach. I also have tried probiotic supplement but I’m not sure that I’ve seen improvement from that either.
She added, “I haven’t had IBS symptoms on days that I have been standing yet!” So it is perfectly clear that this is cause and effect — standing reduces IBS symptoms.
I used to work standing sometimes: I’d simply put a small drawing board on top of a filing cabinet, rather like a lectern, and work away, sitting only to use my desktop computer. Since I had a row of four filing cabinets it meant that I had a huge horizontal surface for paper-shuffling. Nowadays use of a laptop would make everything easier.
When I wear trousers which are too tight I get stomach cramps, too, after sitting a few hours.
Funny thing is, apart from the cramps I won’t notice they are too tight. So when I buy new trousers sometimes I end up with severe cramps and even circulatory problems up to fainting before I notice the clothing being too tight.