No—based on the community answers, neither Lightroom nor Aperture forces you into one fixed on-disk folder structure.

Aperture can either:

• import masters into its library,
• leave masters where they already are, or
• import them into a folder you choose.

Lightroom also does not enforce a specific folder layout. It uses its own catalog for managing metadata and edits, but you can choose where your photos are stored when importing. It also offers flexible folder and file-naming options, including reusable naming patterns.

So if keeping your current folder structure matters, both applications can accommodate that. The main difference is more about workflow style than folder restrictions.

Since you already use Bridge and Photo Mechanic, the best advice from the answers is to try the free trials of Lightroom and Aperture and see which matches your workflow better. Both impose some organizational logic as catalog/workflow tools, but neither requires a proprietary folder structure for your image files.