Yes, the signal can be reconstructed from the spectrogram, provided that:

• you preserve the phase information

• you use classic spectrogram (mel are irreversible unless by heavy compute)

here is described a non-neural k-means clustering vocoder which can reverse specrogram to original with no audible loss of fidelity:

https://blog.hashtron.cloud/post/2025-05-03-take-me-home-to-the-kmeans-city/