For a given quantization level of JPEG compression, are all possible DCT matrices have valid IDCTs. By valid, I mean matrices whose elements are in the range [0,255] ?
All images blocks that are applied by DCT matrix have a valid IDCT - i.e. they can always bring back original pixels and in general inverse transfer is theoretically as well as computationally viable.
However, while your pixels have values in range 0-255 - the DCT matrix of the block never results in values which are confined between 0-255. Not only that, they are not even integers - they are real values. So while they are valid numbers, they can't be stored in the same container as pixels.
Given that they are real numbers, it would be useless to be used for compression against integers of the original source. So hence they are confined in a particular range and then divided by a specific number - this is a process of quantization. Hence, what really goes inside your JPG or MPG are quantized co-eofficients.
The quantization is not equal. Certain components are preserved more than others (with finer quantization) - hence dynamic range of each component, though finite, is not 0-255 but different for each DCT co-efficient. this is practically taken care by Huffman coding which maps these values into binary bits.
So they are valid in 'general' definition but not what you are interpreting as.