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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
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Since the chromosomes would have been on the same chromosome they would might show linkage resulting to a change in his data.

Data obtained would give wrong statistical answers and Mendel wouldn't have ever given LAW OF INDEPENDENT ASSORTMENT