You can tell whether a timeless decision agent would prefer to have been born by giving it opportunities to make decisions that acausally increase its probability of being born.

EDIT: For example, you can convince the agent that it was created because its creator believed that the agent would probably make paperclips. If the TDT agent values its existence, it will make paperclips.

I don't think a causal decision agent has anything that can be called a "preference to have been born".