No Tesco doesn't have an online facility to view your balance - annoying yes but you can "kinda" get a round that by using your clubcard login website -
https://secure.tesco.ie/register/?from=https://secure.tesco.ie/clubcard/myaccount/home.aspx
At the very least you can view your purchases within a few days and track your spending a bit better.
I use the website regularly and call up once or twice a month to confirm that my balance is what I expect it to be. (And yes it's not a 24hr service)
Some people may see that as hassle but I use my tesco credit card for all my purchases and actually don't shop in tesco much (too expensive).
As a result I earn roughly 40 euro worth of points every quarter - which is doubled to 80 euro off my gas bill with Bord Gais Energy.
So up 320 euro off my gas bill a year is worth it in my opinion.
Tesco are slow opening your application and your balance starts off low - mine was initially 1000 euros - but after 18 months I've gotten it up to 3500 euros.
I still keep my AIB credit card - initially because of the low balance - now more for the fact that if Tesco were to pull it's credit card operations from Ireland - I'd still have a backup card with a good balance.
Yes it's costing me an additional 30 euro a year in stamp duty but not fully convinced in giving it up just yet.
Also their posted monthly statement arrives usually late - however this doesn't bother me as I have a direct debit set up and will also use MyBills.ie to clear my account from time to time.