Yes
Look at the 'restricted items'
You can take in a sealed bottle of water, or an empty reusable bottle.
You can take in food but they basically say enough for you and 'no branded items' I think this is so if you are eating no one is getting free advertising.
There are lots of free water stations and at the NEC there was at least one drink vending machine.
If you are travelling from the North then Wolverhampton has a huge, open 24 hours, car park at the station.
www.sabaparking.co.uk/car-park/wolverhampton-station-car-park
Virtually all trains south from Wolves stop at Birmingham New St, if you get a fast train it's 15 mins and one stop.
To get to Birmingham international it tends to be slower trains so 30 - 45 mins.
There is parking at Birmingham Airport but that isn't a cheap option.
To get to Central Birmingham from Wolves you can also use the tram, Either from the city centre, or from Priestfield station, that has quite a bit of parking.
Personally I prefer the tram, it has level access and is much more open than the train although it takes about 30 mins to New St. We used the train because the tram doesn't go to the NEC.
If you are driving down the M6 and want to use the tram get off at J10 and head to Bilston.