They're important. How much so depends on what kind of recurve you're talking about. My wooden recurves have radiused bellies all the way to the tip, and they're narrow... so upon release, I'm asking the string to return down the center of a recurve with a narrow, round belly surface. Without the string grooves on the belly, the string would likely roll immediately off the limb and the bow may not survive a single shot. This perhaps 'epitomizes' the NEED for the string groove on a recurve.
Even on 'regular' glass/wood laminated recurves, the grooves are needed to keep the string centered. Without them, even a Perfectly Aligned bow can be drawn and let down with the string off-centered if the handle is torqued to the side just a little bit. If the string is off centered, the tips will be pulled out of alignment and will point to the side.
Try this, take a recurve and pop the strings out of the grooves and off to the side and then look down the limbs and you'll likely see the tips being pulled to the side. It doesn't take much to have an effect... just the width of the string. Many folks leave their recurves strung all the time. If stored that way, with the limbs being pulled to the side by an off-center string, what do you suppose the result might be?