Yes, in theory it's all protected by a 13A fuse so "can't be overloaded".
I practice, a 13A fuse can allow a considerable overload for a considerable period of time before blowing, so it's best to avoid the scenario where it and the wiring it protects is likely to be overloaded, especially where more wire than designed has been rammed into the terminals of the socket strips, so you may get poor connections which will get hot. As said, 4 way strips like that tend to be engineered down to the lowest cost possible as it is...
For a fixed installation of 4 way strips like that I would use a fused spur box to feed each one and extend the ring main to feed the spur boxes. That way, you're not ramming 2.5mm T&E into the terminals in addition to the flex they are designed to terminate.
Better still, fit a pair of proper 2 way 13A sockets on the ring main at each location and bin the 4 way strips, or use them occasionally as extension leads as they are designed to be used.