Well it might do on this guy’s monster but for most of us, if you haven’t updated your website in the last couple of years, then I’m betting that the answer to this question is no, or probably don’t  know because you haven’t checked it.
The last few years has seen an explosion in the use of such devices, by which I mean, tablet computers and smart phones. Moreover, the use of these devices to view websites seems to be on the increase. Stats from some of our clients’ websites are showing up to 60% of all visits coming from hand-held devices. So I recommend that you check out your site as soon as possible.
What  should you be looking for?
The main difference between desktop/laptop computers and hand-helds is the smaller screen size. Especially so with smart phones. Generally speaking this means that your site should be able to fit on the screen without having to scroll sideways – a major no no! At the same time it must be possible to read the  site. In other words, text shouldn’t be so small that a visitor has to resort to a microscope to read it.
What does this mean in practice?
Unless the pages are extremely simple and sparse (a la Google for example) then the site design needs to be responsive. In other words, the page window narrows in width to fit the screen so that the visitor doesn’t have to scroll horizontally. Good responsive designs allow the images to shrink but at the same time keeping the text to a readable size. If the site has multiple columns good designs will automatically reduce the number of columns, stacking them vertically rather than leaving them in place to shrink horizontally indefinitely. A web page with 6 columns remaining side by side as they shrink to fit a smart phone is not going to look good.
So what should you do?
Firstly take a look at your site on a couple of  tablets – an iPad and an Android device if you can. Also take a look on a couple of smart phones.
You can also check if any page on your site is mobile-friendly using Google’s site checker here.
Then if the site looks terrible, or the Google mobile-friendly checker fails it, Â get hold of your web developer and ask for a quote to update your site.