Hi Nathalia,
I don’t have any knowledge about .svg’s and import/export, but I think it will depend on the logo.
What you should probably not do, is Convert it to a Mesh!
I did a small test:

Extrude and Bevel on the Curve and add a Deform Modifier (here a Lattice).
But some .svg’s consist of several Curves and then things might be a bit more complicated (or not…I don’t know)