Yes, parents should allow their children to have relationships in college, because relationships are how children learn to communicate with each other. Relationships are one part of growing up. Most college relationships don't work out, but children can learn from the ones that don't, and can figure out what they want in a long-term partner.
While parents have the ability to monitor and control what their children do up to a certain point, college students are typically 18 and above, and thus they are legally adults. Along with adulthood comes the legal right to make certain decisions, even about marriage. However, if parents are paying for college, they can certainly set parameters, such as saying they will cut support if their children aren't maintaining good enough grades because they're overly concerned about their significant other. Also, parents should also explain that college peers may put a lot of pressure on them to do certain things, including getting engaged by senior year, even if they really haven't really found Mr. or Miss Right. Just because they may date in college, it does not mean they should follow what their peers do.