Yes, I believe this has the same (not very good) scaling as the long-bond approach. In fact, I think this approach will be even more highly entangled than the long-bond for the purpose of simulating a 1D system, since the bulk of the system will have two "copies" of the 1D chain running through it!
As you may know, the reason PBC is tough with the usual DMRG approach is because the standard DMRG algorithm is based on a matrix product state form of the wavefunction that is suitable for open boundary conditions. That is, it optimizes an open-boundary MPS. So if you input a periodic Hamiltonian, it can work but it will be sort of a mismatch between the type of Hamiltonian and the type of wavefunction.
One could also optimize a periodic MPS, which could in principle give a better scaling algorithm, but fewer techniques are known for periodic MPS and it's not known how to optimally truncate them just using local operations or how to achieve similar algorithmic properties like "gauging" an open MPS to make the eigensolver step have nice properties.