Do covalent salts produce sodium carbonate extract? In case of qualitative analysis of anions, sodium carbonate extract is prepared for insoluble salts.

It is done by heating (for 10 minutes) an aqueous solution of a mixture of the solid salt and sodium carbonate in 1:4 ratio (by mass). As far as I understand, the principle behind preparing sodium carbonate extract is to prepare a clear solution containing the anion by precipitating the cation as insoluble oxide or carbonate.

But is this process applicable for salts that do not ionize at all in water, or covalent salts like $\ce{SnCl2}$, $\ce{SbCl3}$ etc.? I have never tried this myself.
Soda extract is done to remove multivalent cations from your sample solution, by precipitating them as (mixed) carbonates and hydroxides. 

Antimony or tin chlorides are well soluble even in water, and even if the solids have a strong covalent character, they are still ionic in solution.

The sulfates of barium, strontium and calcium are however very badly soluble, so it doesn't work for those. You can however do it in the melt, instead of solution. After cooling and powdering that melt, you add water. What dissolves are sodium sulfate and soda. Add $\ce{BaCl2}$ to detect the sulfate. The residue are the alkaline earth metal carbonates, which dissolve in $\ce{HCl}$.

(Please check your textbook/lab manual for the actual procedure. I have Jander, Blasius, Einführung in das anorganisch-chemische Praktikum. Perhaps someone else can recommend a good English book.)