Clear answer: It depends
Generally, yes. Larger sample volumes mean that your sample reaches the column in a larger solvent "plug". The larger the injection volume, the wider the peak will be. Wider peaks means less resolution.
And now the BUT: If your sample solvent is weaker (meaning less elution power) than the mobile phase, the sample will get concentrated on the column head as it reaches the column. This is especially pronounced with gradient separations, where the initial mobile phase is too weak to significantly move the sample. Therefore, with gradient separations you might be able to actually inject rather huge sample amounts without significant peak broadening if the sample solvent is weaker than the initial mobile phase.
In the end, you have to try. Occurence of peak broadening or distortion because of a too large injection volume is a complex function of solvent and mobile phase composition, column dimensions, flow rate, injection volume (obviously

) and even the HPLC itself (tubing dimensions etc.).