I would think that the chain is long enough, but as HillRider points out carefully try shifting into the 53-27 combination, with no rider on the bike. If in the big to big combination the derailleur doesn't "bottom out" you should be OK. No need to change derailleurs. You could also replace the 39 inner ring with a 38. It's also possible to make or buy a custom cassette with a larger big cog, like a 13-28, or even a 14-30, but it may take some tweaking to get the D-A rear derailleur to work with a 30 cog.
Al