Maybe the chain is long enough but if you put old chain on new sprockets, sprockets wear out pretty quickly. So I recommend that you buy new chain for new sprockets
My wife rides a 2007 ec200 I want to change the std 13/48 gear ratio to 13/51 , will the std chain be long enough or do I need to get a new chain ?
Stock GG sprockets and chain are very good in my opinion and i would just gear according to your needs. I have two sets of wheels and am still on stock chain and sprockets on both sets after several thousand miles of races and riding.
Fit a 12 tooth same as 13/51 and you know it will fit. after that's stuffed go out and get the 13/51 chain sprocket setup.
I would stay with the 13/48 on the 200 as going up on the rear will not give you the results that you thought it would, I tried a 50t and then a 52t and hated it, went back to the 48t which holds a gear way longer. If you want more snap change the muffler to a DEP and get the jetting right...all good.