If you are refering to Mobil-1 motorcycles oil (not the regular Mobil 1 with friction modifiers) it will NOT hurt anything. Wether it makes sense to use it is another thing.. The great thing with synthetics is that they take a lot longer to break down than Mineral oils, but they cost a lot more. I always use synthetic oil in all my vehicles but you have to decide what you want to do. If you are going to change the oil every 4000 miles (as I do) I would just use a good dino/mineral oil, but if you want to push the changes out to 8000 or 12000 miles then a synthetic is definately the way to go.. Using a synthetic and changing it every 4000 miles is just a big expense for no benefit (But I still do it!!
), good Mineral oils work fine for 4000 miles and cost a lot less than synthetics.. You can definately switch over to Mobil-1 and not do any harm to your engine but it's not worth the switch IMO if you keep to the regular Honda recomended oil change periods..
Having said that I don't do what I am preaching as I can afford the synthetic oil and like the extra peace of mind that I think it gives me.
As mentioned everyone has their own opinions, but my father in law has been in the oil industry for over 50 years and that was what he told me and I believe he knows what he is talking about (I have tremendous respect for his knowledge on oils and engines!).