A diaper bag counts like a purse, not like a backpack-- they will check the diaper bag as well as the stroller, but YES they will let you bring both in. They will even let you store the stroller in the handicapped open seat areas. Pro stadiums are actually pretty kid friendly because the stadium employees who work the entrances and gates are used to kids.
When they check the diaper bag they will let you bring in things that are directly related to the baby (formula, bottles, etc.) but will NOT let you bring in anything THEY sell (bottled water, sodas, chips, etc.)
When my kids were less than a year old, the noise bothered them more than they bothered the other audience members-- bring some of the soft yellow kids earplugs, or plan to sit outside the 40's so the sound is not so "in your face".
FYI, bring extra bottles or sippy cups-- because as the noise bothers the baby's ears, they will need to "swallow" to readjust their ear pressure just like you do when you fly with the little ones.
Last, if your wife is nursing or needs a more quiet area to soothe the baby at any time, ask one of the stadium officials, they will usually let you retire to a press lounge or empty stadium box.
Hope this helps. I've toted my kids along with me everywhere from DCI shows to the symphony and as long as you are prepared ahead of time, it always works out.
Heads up for the fans who don't like children at events such as this-- you'll get your share of nasty looks... and get just as many smiles from other parents who have been there. :-)