Not really. The blockyness in JPEG images is from throwing away less significant terms in each 8x8 pixel block to save space. Any lossy image compression method will cause artefacts of some kind, no matter what transform or system it's based on, but JPEG's ones are particularly artificial-looking as they're square and lead to sharp visible edges. Some other methods of throwing away information aren't based on blocks and just make things blurry.
AFAIK the main source of blockyness is due to the quantization of low-frequency components, such that the decoded signal doesn't quite match from one block to the next.
The ringing around edges in the source signal, Gibbs phenomenon[1], is due to almost or entirely discarding higher frequency components.
