Q. Can you install the latest VDA for XenDesktop on VDI-in-a-Box? 
A. You can install the latest VDA for XenDesktop on VDI-in-a-Box.

Additional Information

The latest version of VDI-in-a-Box is 5.4.4 available here: https://www.citrix.com/downloads/vdi-in-a-box/product-software/vdi-in-a-box-54.html.
The fixes included are here: http://support.citrix.com/article/CTX134622 (VDI-in-a-Box 5.x - Issues Fixed in This Release).
The upgrade documentation is here: http://support.citrix.com/servlet/KbServlet/download/37127-102-709281/VIAB_Hotfix_Upgrade.pdf
The XenDesktop 7.1/7.5 VDA hotfixes can be installed with VDI-in-a-Box version 5.4.4 during the Edit Image stage when creating a new image or updating an existing one.

Can you install the latest VDA for XenDesktop on VDI-in-a-Box?

https://www.citrix.com/downloads/vdi-in-a-box/product-software/vdi-in-a-box-54.html
http://support.citrix.com/article/CTX134622