Jimmie,
No, I think if he learns from an early age not to go off the side of the bed, then he is safe playing on top of it. Some rats I have heard of love escaping down the side of a bed or couch but other rats have no interest in that and have a self-preservation/cautious attitude about that. It can be different for different rats. In our case, when Klausse and Wolfgang were very young and we had them out for free play on the bed every day, sometimes when they got curious and went sniffing out over the edge of the bed, we would just gently nudge them in a direction back from the edge of the bed. They were probably the type of ratties that got a little apprehensive about going down the side of the bed, and we also supplied the little directional nudges away from the edge that sort of reinforced the idea that going down the side is not good. They never had any inclination to jump or crawl down the side. But, that is just my experience! If you are there during his free time on the bed and you sort of put your hand out by him to direct him away back toward the center if he gets curious out at the edge, he will get the idea that the sides of his play area are off-limits. Hope that makes sense! Of course I have seen other rat parents talk about their rats always trying to get down to the floor, so there ya go! All rats are different. Rats in general prefer staying close to their people, especially when they love their people bunches!
One time, when my husband was sitting with Klausse in his office chair and had Klausse on his lap, he slipped off of my husband's lap and plopped down to the carpet under the chair. Not a long fall, and he was fine, but we were amazed that Klausse was momentarily on the floor of our living room and sort of looked around in a circle, then looked up at my husband and waddled over to his feet, looking up at him, like a loyal dog, as if to say, "Um, I fell down...can you pick me back up please?" It was the sweetest thing. So, our boys loved being near us and did not have a desire to run off. But, that is not always the case. Depends on the rat!