Is it possible for the iodine atom in periodate ester to be octavalent?
I would suggest that a reactive intermediate/transition state was formed, and not an actual compound. I'd say both $\ce{C-O}$ bonds are partially formed in the intermediate



The diagram in the book does not show where is the $\ce{Na+}$ during the reaction (see above picture), probably for the convenience (but therefore, somewhat misleading). Remember, a periodate ester is an ester of periodic acid.  The most common periodate esters are cyclic periodate esters, form as the intermediate in oxidation of vicinal diols such as sugars and glycols. For example: The oxidative cleavage with periodic acid has been successfully applied in the constitutional analysis of sugars (see: Chemgapedia article). 

Experimental evidence for presence of cyclic periodate esters (rightfully with hepta-valence iodine) can be found in: Buist, G. J.; Bunton, C. A.; Hipperson, W. C. P. The mechanism of oxidation of α-glycols by periodic acid. Part X. The oxidation of pinacol, and a general discussion of the stability of periodate esters and their role in the mechanism of oxidation. J. Chem. Soc. B 1971, 2128–2142. DOI: 10.1039/J29710002128.

Also, two forms of periodic acids can be found in the corresponding Wikipedia article.