Simple answer: NO. If you do that, the most likely bugs you'll get as tenants in there are all sorts of wasps, hornets, wax moths, etc.
Explanation: Native bees are usually what is called "solitaries", meaning they do not congregate in hives of thousands upon thousands. They usually go about their business finding food for themselves and their brood, have their own nests, some in thick bushes, some others burrow holes underground or in lumber, etc. And even though they feed on nectar and pollen, they do not produce/store honey in their nests. The only bee variety to produce and store honey in amounts useful to humans (or other beasties) is the honeybee, commonly the european variety. The native bees' most notable benefit to humans is their incredible pollinating capacity. And the easiest (and most natural) way to get a

-truck-intercourse load of pollinators for your fields is to make pollinator-friendly spaces around your field(s). That means, plant (or allow to grow wild) a variety of flowers, tall grasses, weeds, milkweeds, etc. and as possible, try to plant or let grow native, non-invasive plant and flower varieties. Native to your region, that is. We have done that in our backyard Right in the middle of the city) and you'd be amazed at the amount of native bees, bumbles, butterflies and other pollinators you can find in it on any day.
The only way you could (stress on could) get honeybees from the "wild" is by catching a "swarm" of honeybees (which includes their queen) that have just and left a domestic hive and gone feral. This usually is a long, complicated and many times unsuccessful, process... I have gone through quite a few myself, but that's a story for another day. Another way is by hunting for a "wild hive", those you see in the TV shows that have built their hive inside the walls of a house or the trunk of a hollow tree. And then you have to retrieve them and put them in a hive box to start a colony, assuming you were able to find one to begin with. In either case those feral honeybees you may find will almost always trace their origins back to a nearby domestic hive that swarmed and was never caught and re-hived.
Bottomline, these avenues most always end up being infinitely more complicated and fruitless than just buying a domestic starter colony, queen and all.
If, however, you are inclined to having bees that actually produce honey, (and by extension pollinate everything around them), wax and other goodies, the best way I could recommend is to contact a beekeeping association locally and asking them if they or any of their members can sell / trade / donate to you a nuc (pronounced "nuke")/starter colony, which should include a Queen.
VERY IMPORTANT: wait until the end of winter to actually get the bees. Right now is harvest time and prepping the hives for overwintering is only a few weeks away. Once they finish stocking up on pollen and honey/nectar to feed from over the winter and the hive is closed/wrapped, all they will do is hunker down, ball around their queen and keep her and the hive warm and alive until the snow thaws the following spring and she starts laying again.
Starting a colony as soon as favorable weather allows in spring is the best way to make sure it gets established properly and has the best prospects for a healthy lifespan. And unless you have some experienced beekeeper at your beck and call 24/7 to care for the hives, get started with JUST ONE hive. You'll see what I'm talking about when the time comes. Anyway, If you decide to go that way and / or the pollinator-friendly spaces, give me a holler and I'll be more than happy to try and help you through the process and all the prep / installation / maintenance details.