Diode OR 4 batteries
No, a diode circuit as you describe won't automatically balance the load across the batteries in the manner you describe.

Note that everything below this comment only applies if those packs are raw LiIon packs with no internal regulation.  If they're internally regulated, then all bets are off.

It'll work more to keep the state of charge of all four batteries more or less equal as they discharge.  However, if you have three bad batteries and one good one, that good one will take the load.  If you have three halfway discharged batteries and one fully charged one, that fully charged one will take the load.  Etc.

There's a good chance that if you take pains to get lots of four batteries and use them together (i.e., charge them at the same time and always load all four at once into your rig) that a simple circuit as you describe will mostly do what you want, because the batteries' voltages and the diodes' drops will be close enough together that the batteries' internal resistances will handle the match.

If you want to absolutely enforce a rule to "don't take more than 10A from any battery, ever", then you'll need some sort of fancy power supply management circuit, and it'll probably have to be custom made for your purpose.