Is there a way to convert stud.io files into LDD files? Is there a way to download stud.io files from Bricklink and convert them into a format that Lego Digital Designer understands?
Yup.


Both programs (Stud.io and LEGO Digital Draw) can read the LDraw extension (*.ldr).


Overview:


I'm using Windows 10.
I have NOT ungraded to the Stud.io 2, but I think it shouldn't matter
in this case.
In Stud.io, we will be exporting the file into the *.ldr format.
In LDD we will be importing a *.ldr file to be readable in LDD.


The Method:


Download ".io" file from BrickLink to your PC.
Open in Stud.io. and export save as a .ldr file. 
(File > Export As > Export As LDRAW...)
Open LDD and import file. (File > Import model) Here you will also have to toggle the file format, *.ldr, you wish to import.
Find your *.ldr file and get to modifying.


Know Annoyances: Ghost Switching 1x4 Bricks.  Tubeless vs. Tubes files.

The final leg is to order your model through Bricklink via Stud.io, but Stud.io can't recognize the default tubed version of this 1x4 Brick. So, you'll be saying to yourself, but I've never used this tubeless version in my build, so what gives? 

Apparently, the conversion into the LDraw format changes tubes into tubeless. This is annoying becasue it's not immediately clear why you're not able to find sellers for 100% of your wanted pieces, not understanding that a switch happened early in the conversion process. 

Just a heads up.  In LDD you could search for these 1x4 tubeless pieces, and manually switch them out to tubed then re-save the file, or just mentally note to add the proper amount of tubes pieces in Bricklink.  Either method is just as annoying as reading this brick of text...

See  ya!