This paper proposes a strategy to overcome the threats posed to connectivity-preserving synchronization of Euler-Lagrange networks by time-varying delays and bounded actuation. It first introduces a suitable distributed negative gradient plus damping injection controller, based on which it establishes that the local connectivity of time-delay Euler-Lagrange networks can be preserved by appropriately regulating the interagent connections and increasing the damping injection locally. Yet, actuator saturation may impede the proper modulation of the interagent connections and the injection of sufficient damping and, thus, may threaten the maintenance of connectivity. This paper then develops an indirect coupling control framework which integrates the bounded actuation constraints into the control design. The framework endows every agent with a virtual proxy and couples initially adjacent agents through their virtual proxies. The interproxy couplings then tackle the time-varying delays while the agent-proxy couplings account for the saturation of actuators. Lyapunov-Krasovskii analysis proves that the indirect coupling strategy can drive time-delay Euler-Lagrange networks with bounded actuation to connectivity-preserving synchronization by limiting the energy of the agent-proxy and interproxy couplings according to the actuation constraints. Experiments with Geomagic Touch haptic robots validate the proposed designs compared to a conventional proportional plus damping controller.