Probably. Yeah, I know, terrific answer. The problem is that "Sheesham" is Dalbergia sissoo, a known wood. "Golden rosewood" isn't an actual name as such. It's like using "golden oak" to refer to a color rather than wood from the actual Golden Oak tree (Quercus alnifolia).
This site was very helpful - http://www.regencychess.co.uk/chess_woods_guide.html
I just received an email that the House of Staunton has released their Dubrovnik set in Golden Rosewood.
Is Golden Rosewood the same wood as Sheesham?
It is nice to see HOS has a set with the darker pieces being more of a brown color as the Fischer Dubrovnik had.
Now, all 3 makers of Dubrovnik sets have a brown wood offering, Noj has Walnut or brown stained, Chess Bazaar has Sheesham and now the House of Staunton has Golden Rosewood.