Well they never give a profit breakdown in their results which suggests it isn't.
Also, paying someone to pick items off the shelf and paying another person to deliver the items to your home has a cost and that cost is not covered by how much they charge for service, which for regular subscribers is negligable.
The grocery market in the UK is highly competative and margins are quite low.
Tesco's share price has done well recently because of take-over speculation after the recent Morrison's buy-out. Other than this it's performed relatively poorly for the past 10 years.
As already mentioned, they don't publish seperate profit and loss figures for home deliveries. There is a good reason for this.