Can we form any circuit using half adders only? (assuming we have as many half adders as we want)
Sure you can, but why would you want to?

A NAND gate is a universal gate, as you have agreed. Here's how to form a NAND gate using a Half Adder:







simulate this circuit &ndash; Schematic created using CircuitLab

That said, a NAND gate is the simplest two input gate you can form, at least in NMOS/CMOS, so it seems like a rather backwards step...