Sweet Cherry, Prunus Avium. or wild cherry might as well also be known as Bird Cherry because these trees can grow to a massive 105 feet eg a 10 story building, leaving all the fruit to the birds. Even the shortest cultivars are 50ft specimens. thus they are always grown on a root stock that will dwarf their growth.
The natural cross and chromosome doubling with the 3-6ft tall prunus fructose gave us the sour cherry with its more modest respectable height of 13-32ft. And their propensity to not require a mate to set fruit.
But there are few sweet cherries that will produce fruit without a partner, Benton, blackgold, lapins, starkrimson, stella and whitegold are all sold commonly in the garden center. And if you have one its seedling will likely be a monster. However, it may or may not maintain the self-fertile so it might be forever looking for a mate.
Unless you let the rootstock fruit, it’s likely not close to the rootstock.
The fruits from the seedling will likely resemble the tree the pit came from in some degree. But can be quite different. (see below for explanation)
Hard to tell without more information.
Are there other cherries nearby? Do you know what cultivar the tree the cherry pit came from is? What other cultivars are nearby, and thus possible pollinators. And just to be sure. You have a sweet cherry right? Not a sour cherry or canadian cherry? (the “sweet” in sweet cherry does not only pertain to the taste of the fruits, but to the specific species prunus avium. Where other cherry species grow differently and are quite different from P. avium)
The genetics of the seedling is determined by
-the mother tree
Most cherries are self incompatible. But not only that, they can be incompatible with other cherry cultivars to.
Check this document for compatibility groups.
Most fruit trees are not true breeding. Most are hybrids of hybrids. Thus the fruits from seedlings can vary quite a bit from the father and or mother tree.
And even if you have a cherry that is self compatibly (can pollinate itself) the seedlings from those pits can vary significantly from the mother tree.
than you can expect the seedling to look somewhat like a mix of those 2.
However due to the parent not being true to type breeding wise. There can be large differences and there is a decent chance the seedling is quite different from either parent.
either way, i myself won’t keep the seedling as is. Since it would make a really large tree (unless you have room/want for that) but graft it to either a smaller rootstock. Or a side branche of an existing tree. That way you get fruits way sooner.