Actually not, imho. This remains a two stage compressor running on energy from exhaust gas. The number of turbines and compressors is the same as regular setup. Perhaps series linked turbines running on exhaust extract more total waste energy from exhaust. But the second turbine creating back pressure reduces the extraction by the first turbine. So you take a turbine out of exhaust series, and plug it into the compressor series. Energy extracted by LP turbo increases, possibly more efficient than two turbines in series. Yes, you lose the compressor efficiency from the low pressure turbo - the drive gas for the small turbine is that much less dense. But if energy recovery by the primary turbine is more efficient, it compensates a bit.
The energy used by the small turbine here would normally be dissipated by the intercooler. Nobody complains about that loss, usually! So basically you are recapturing a bunch of the adiabatic loss from the LP compressor, and using that to drive the second one, in part.