Last week in Edinburgh, Sainsbury's gave a resounding yes as it launched its now wholly-owned bank after completing the buyout of 50% owner Lloyds a fortnight ago.
Its development plans could see Sainsbury's shoppers offered a computer booth and a Skype-style link to a financial adviser, as the bank seeks to grow its 1.5 million customers, using its 23 million store visits a week.
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In a survey for the bank, 57% of Scots said they now spent more time researching and shopping around for their banking and insurance needs than they did three years ago, and around 20% would consider using the supermarket banks. Across the UK, more than 40% of those looking for new credit cards, personal loans or pet insurance policies would consider the supermarket banks.
David Black at Consumer Intelligence said of the supermarket banks: "Through having numerous frequent shoppers in-store or online, they have significant opportunities to market their financial products."
The new TSB may be looking for the high ground with its "local bank" pitch, but the supermarket banks ramp up the stakes with their loyalty schemes. Sainsbury's offers discounts and preferential rates for Nectar card-holders, double points for two years on selected buys, and the equivalent of 7% back on all their Sainsbury's shopping for anyone buying all six insurance products.
M&S Bank offers discounts and vouchers linked to its expanded range, which now includes a £10-a-month fee current account offering preferential rates on other products. Tesco, the only retailer to offer mortgages, links loyalty to its Clubcard. It claims to sell financial products to one in five of its shoppers (compared with one in 20 at Sainsbury's), and says they typically spend 12% more on their shopping once they are a bank customer.
Sainsbury's current personal loan rate of 4.6% (for loans of £7500 to £15,000 over three years) is joint lowest in the market, ahead of Tesco and M&S on 4.8%. There is also more to insurance than just price, and Sainsbury's stresses that its car and pet policies offer a quality of cover limited to 5% and 2% of policies in the market respectively.
Its Nectar credit card is among only 1% of cards offering 0% on both balance transfers and purchases for 15 months (and a double Nectar reward scheme). However, Tesco offers an 18-month free ride on purchases. Both the big two are in the top six deals in all three credit card categories listed by Moneyfacts.
Sainsbury's said it has no plans to launch a current account in the wake of Tesco, which plans to launch its range of accounts this year. It has outlawed staff sales targets and product bonuses to boost public confidence.
Sainsbury's Bank's new chief executive, Peter Griffiths, who used to head the Principality Building Society in Wales, said there is a "huge opportunity" for the bank. He said: "The consumer has shifted significantly, particularly youngsters, around value-sets. They are very choosy who they want to work with and look at a company with far more rigour."
And Sainsbury's head of corporate affairs, Alex Cole, insists: "The fact you have a Sainsbury's close to you makes you feel close to the brand."
However, one leading retail analyst suggested last week that faltering sales among the big supermarkets since Christmas was a sign of growing "anti-corporatism towards the major players".
Clive Black of Shore Capital asked: "Is there a growing collective distrust and disconnection with the dominant brands that is leading folk elsewhere?"
Griffiths said the demise of financial advice in the banks has paved the way for online advice services, adding: "I think we can build a trusted face-to-face service, delivered remotely."
But he said: "I am agnostic at the moment as to what our store proposition needs to look like."