Raman Scattered (inelastic) photons rescattering outside of capture area
Yes, of course the Raman scattering can suffer from additional scattering on its way through the sample, just like it will generally be attenuated on its way to the detector by any element in its path (mirrors, lenses, glass surfaces, etc.). 

If scattering is a problem or not very much depends on your sample. The ideal sample will not scatter your excitation laser or Raman scattering much, like for instance a clear solution, and then I would say the influence on the measurement is negligable. If you have something opaque, such as an emulsion, additional scattering will be relevant and you would want to measure near the sample surface.

If you have problems with a glass-affected background you could switch to quartz glass or use a confocal Raman setup, if available.

And also depending on your sample, absorption might be something you should consider as well.

By the way: I would probably rather go for a planar glass surface in order to avoid refraction as it occurs on a curved glass surface.

Edit due to comments:
Pure water does neither absorb nor scatter light with a wavelength around 532 nm much. If it would, you would be able to see this with your eyes. Wikipedia claims that a fraction of 10-7 of the incoming light is scattered inelastically. Although this should be only used as a rule of thumb, this tells you that a loss of Raman intensity due to "secondary" Raman scattering is not a practical problem you would usually be able to observe. Also, I would not be worried about elastic scattering although it is much more relevant than inelastic scattering (Wikipedia claims 0.1% to 0.01%). 

I do not know your Raman setup in detail. But if you have anything like a confocal aperture (pinhole, slit...) on the path to the detector, refraction on the container/water surface will definitely reduce your signal intensity with increasing penetration depth, especially if you do not measure with an immersion objective lens. This is because your focus is severely distorted especially in length when focussing deeper into the sample, it will become much longer. Your confocal aperture then blocks part of your signal because it originates from a part of the sample which is far from the focal plane. This is descibed in detail for example in this paper, and also in this paper. However, the papers are behind a paywall.