Yes if characters he selected were present on the same chromosomes then there were chances that he would have missed law of Independent assortment.
Independent assorment and Linkage are the two concepts that relate to DIstance between the alleles
If alleles are present on the same chromosome they have a tendency to show linkage depending upon their distance. Less distance between the two more are the chances for linkage
So choosing such characters definitely would not have allowed Mendel to reach at the same conclusions.He was lucky in choosing those traits in pea plant