Sure they would, they could have been quite effective and a few were actually trialled. The problem was that for any type of shield to be effectively bulletproof it had to be a certain thickness. This made any type of steel shield very heavy, even on wheels. So a shield would have to have been so small as to be light enough to be moved that it would provide negligible cover to any more the a couple of men. The other problem was that the land the shields would have to cross was very rarely flat. No Man’s Land was usually pockmarked with shell craters and ideal defensive positions were usually on top of hills or rises in that land, necessitating attacking forces to push these heavy shields uphill.

Now eventually someone came up with the idea of putting a motor on a big metal box and putting men inside. Then they added tracks to accomodate the broken ground and then they decided to put guns on it. By 1916, they didn’t need shields, they had tanks starting to appear on the frontlines. By then it was a matter of improving the reliability of these new weapons and working out the best ways to use them.

Just to add onto what /u/TheWellSpokenMan said, I highly recommend browsing this book. It's called "Helmets and Body Armor in Modern War" by Bashford Dean. Mr. Dean had actually designed some experimental armor for the US during the war (it was rejected in the end, the helmet was too similar to the Stahlhelm and the armor was generally impractical) and wrote about experimental armor that was used during the war.

There are lots of images, and in fact, he shows a portable shield that the French had tested at one point! The chapter on shields starts on page 178. Page 151 shows an Italian soldier using body-armor as a rifle shield.