I'm wondering if one can (potentially) get any quantum advantage with $R_y$ single-qubit rotations and $CNOT$s only? (Note that I don't care about having a universal quantum computer.)
It is well known that quantum computing with real numbers (i.e., only states & gates with real entries) is as powerful as quantum computing with complex entries. (While you obviously cannot prepare any quantum state, it is computationally equivalent, i.e. you can carry out all the same computations -- which take classical inputs and return classical outputs -- at almost the same cost.)
See, e.g., https://arxiv.org/abs/quant-ph/0301040
Now whether the gate set you propose is universal, I can't tell on the spot -- you would have to check whether you can use it to implement a universal set of real gates (such as Hadamard and Toffoli).