I doubt it. It may, but since you haven't gotten too far in training, probably not. In fact, it may help for him to have a friend who has been through it. You could also ride the new horse in front of him so he knows what to expect.
Have you introduced the bit/bridle yet? I would give him at least a couple weeks with the bridle before you ride him for the first time. I would also at least make sure he can walk trot canter and halt (on the lunge) completely by voice command (not whip!) before riding. I trained my mare (she is now 5, but was 3 at the time we started and had absolutely no training or handling other than being groomed, fed, and led to and from the pasture before I got her), it took me 4 months to put her under saddle, (mainly because I intended to train her to drive first, but she put up too much of a fight.. I didn't think teaching her to drive was worth ruining a cart that cost a decent chunk of cash!) but I wanted to take my time with her. I spent a month lunging her and 3 months of long lining and attempts at dragging the ring, dragging poles, and other shenanigans to try to "prep" her for the idea of driving. If you haven't trained before, I encourage you to take your time. I don't regret it one bit with my mare.