Many website content management systems, out of the box, act like blogs and quite prominently on the page include details of the author and publication date. I’d suggest that you really don’t want these, on a business website. It should be quite easy for your website designer to remove the ‘metadata’ from public display.
There may be a small benefit to seeing a very recent date on a page as far as customers and prospects are concerned. People do worry that much of the stuff they see online could be old and no longer valid, and seeing a recent date is reassuring. But when they click through from a search engine and see a 5-year-old date, it’s quite possible that they’ll hit the back button and try something else, understandably. If the information is still valid, that would be a shame.
As far as search engines go, it doesn’t matter. I’m certain they’ll date a page from when they first saw that URL and content, not from any date showing on the page.
So if it’s a choice between showing the date or not, I’d say not. However, if you wanted to have the date showing for a few weeks or months, and then remove it (either manually or by some automatic means), that could be a productive strategy.