Given the chemical solution: na2co3 + agno3 will a precipitate be formed?

First we have to establish the chemical reaction. As a result of adding Na2CO3 and AgNO3 products formed are NaNO3 and Ag2CO3. NaNO3 is a soluble substance when dissolved in water. 
As a general rule, most Ag, Pb and Hg(I) compounds are considered insoluble. Ag2CO3 is insoluble in water hence the reaction given forms a precipitate. 

Yes it is true that a precipitate will form via the chemical reaction given in the question. The products that will be formed via the chemical reaction of Na2CO3 and AgNO3 are Ag2CO3 and NaNO3. The product Ag2CO3 is insoluble in water and hence will form a precipitate, while NaNO3 is soluble in water.