No, it isn't natural at all.
If the business involved a choice of products or services that were on a sliding scale of cost, a tradesperson might ask a customer what their budget is, and then quote them the options that were within their price range, but we would not call that a 'rate'. A 'rate' is normally an hourly, or daily rate for labour, or some other task-specific 'fixed rate'. A tradesperson sets their own 'rate'. Some may be somewhat open to negotiation on price, but it would not be common to ask a potential customer how they feel about the 'rate', because that is unlikely to change. For example, if a tradesperson was quoting someone to supply and fit a new kitchen, they might help the customer select fixtures and fittings within their budget, but the fitter's 'rate' for labour would likely be the same whether the customer chose a cheaper or a more expensive product. With your example of repairing a car, I can't imagine that there would be options - a specific part, or parts would be needed, and the work to fit them would likely be priced based on the estimated time involved at their fixed rate.