Nope, for two reasons.
First, simply because the contents of the bag aren't held in any kind of stasis. A fireball spell is somehow put in? The spell of duration “instantaneous” is over now. It won't be there later, “waiting” to be brought back.
So what would happen with successfully (see below!) chucking fireballs in, is burning up any flammable contents of the bag (they're unattended, sitting there in the pocket dimension, and won't benefit from the PC's own saving throws, after all), and the fireball being done. Opening the bag later will just have… nothing… happen, while the intended target of the fiery destruction looks at the bag-holder funny.
(That's assuming that filling a bag of holding with fireballs doesn't count as the bag being “overloaded, pierced, or torn”, which would additionally spread the contents' ashes across the Astral plane.)
Similarly for other spells of instantaneous duration.
But that is only the least of the hurdles to overcoming this.
The second, more important problem is that the bag doesn't permit free-flowing movement between dimensions anyway, so spells can't be cast into it in the first place for lack of line of sight. The trouble is that the bag's mouth isn't a portal that allows free passive movement of items/air/material/explosions between the bag-owner's dimension and the pocket dimension. The mouth is a magical surface of some kind that is activated only by a creature actively putting or taking objects. (Notice that an action is required to add and retrieve objects, and that the contents of a bag won't spill out if you turn it upside-down.)
This means that, even if a spell is somehow successfully cast “into” the bag (perhaps the caster jumps in briefly?), something like a delayed blast fireball or a similar injurious spell with a convenient timer won't “spew” out of the mouth of the bag at the determined time. Instead, such spells will just take effect in the pocket dimension, never passing out of the bag.
