Yes, the lineshape does matter. The lineshape is dependent on how the signal decays with time. For example, if you do not collect enough points, you will see truncation artifacts (sinc wiggles).
The lineshape is proportional to the R2 relaxation, which is a relaxation process that causes dephasing of coherent transverse magnetization. Increasing R2 will broaden your peaks. Probably the three main contributors to R2 are bad shimming, dipole-dipole couplings, and chemical shift anisotropy. A fourth contribution to R2 can be chemical exchange whereby a molecule can be exchanging between 2 or more chemically distinct conformations. Any increase in R2 relaxation will broaden your NMR peak lineshape.
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