First of all, let's examine what happens when a signal clips: An audio signal can be represented by a string of numbers, so let's say you wan't to record this signal:
0 0.5 1.0 1.2 1.0 0.5 0
But the signal clips, so what you get is this:
0 0.5 0.9 0.9 0.9 0.5 0
See what's up? Suddenly no signal is present above 0.9...
The thing is, when a signal clips you loose information. A byproduct of this is added artifacts, like higher order harmonics (which introduce audible distortion).
When using de-clipping processing, you can successfully remove and/or mask the artifacts, which can make the signal more perceptually acceptable. But you are not recovering the missing data, only treating the byproduct.
So getting back to your questions:
Is there any way to recover the data.
Nope, unfortunately not.
Also, can someone explain to me what difference to the frequency
spectrum the clipping will make?
As stated above (and by Andrés G. Duarte) you'll see added harmonics at higher frequencies.
How reliable is the clipped data?
It won't be a realiable representation of you input data. Whether it is usable, however, depends on the application. For research I would definitely redo the recordings. You are introducing unknown error sources by using clipped signals - and research have enough unknown error sources already :-)