Yes, it is absolutely possible to restring a smaller size Viola into a Violin. You will not damage the instrument by doing so.
Fractional size violins can roughly correspond with smaller size violas, although technically some will be slightly different in length.
- 4|4 Violin = 14 inch Viola
- 3|4 Violin = 13 inch Viola (Violin body often 13 ¼ inch)
- 1|2 Violin = 12 ½ inch Viola
- 1|4 Violin = 11 inch Viola
In most cases if the strings are good you can move the G D and A strings down and add a new E string.
The tension of viola strings run slightly higher than violin strings, so keeping them may be similar to moving to a higher tension violin set, although looking at a string tension chart there is some pretty wide variation of tensions by brand across the smaller size instruments.
Technically the body of the viola is usually deeper than a violin, but in some brands I've seen the only difference between the viola and violin models was the label inside, and what set of strings were put on. The dimensions were otherwise identical.
I haven't personally made a viola, but checking my measurement book it looks like the full size viola top plate is made slightly thicker. For mass manufactured student size instruments I seriously doubt that most models would have a different tooling than the violin plates.
Another difference you may see is the viola bridge can be set slightly higher than a violin bridge would be, up to a millimeter or so for the thicker strings.
If the viola you are converting does have a deeper body or thicker plates, there will be a tonal difference. In the mass manufactured student instrument market it is unlikely that the tonal difference will be significant.
If you have a hand made and plate-tuned smaller viola made by a trained Luthier, then I wouldn't recommend converting it, since it will have been made to respond to the viola tuning and it is better to keep that kind of instrument in the tuning it was designed for.