"One day and that day may never come"
If a company never invoices me, am I obligated to do anything?
No (given that they know how to contact you i.e. you are not evading being invoiced).
That said, you will still owe the money. When/if they ask it to be paid, you will need to pay.
But there is no need to proactively bug them to take the payment. Until invoiced, you can enjoy the money as a zero-interest loan.