The string-length-parameter (\ensuremath{\alpha}) independence of the on-shell physical N-string amplitudes in the covariant string field theory presented by the authors is shown to all loop orders in perturbation theory and for N\ensuremath{\le}d=26. The proof is based on the new invariance of the string action under the field transformation ${\ensuremath{\delta}}^{\ensuremath{\mu}}$\ensuremath{\Phi}=${p}^{\ensuremath{\mu}}$(\ensuremath{\partial}/\ensuremath{\partial}\ensuremath{\alpha})\ensuremath{\Phi}+(${\ensuremath{\Phi}}^{2}$, ${\ensuremath{\Phi}}^{3}$ terms) with ${p}^{\ensuremath{\mu}}$ being the center-of-mass momentum carried by \ensuremath{\Phi}. By making use of this \ensuremath{\alpha} independence, the calculations of the tree and one-loop amplitudes are greatly simplified and shown to reduce directly to the operator formalism expressions. Most remarkably, we find that our pure open-string field theory contains the closed string as a bound state.