Sprint and Verizon have agreements to roam on each other networks. Sprint actually pays out a lot of cash to Verizon for roaming due to the size of their network. Sprint is tired of having to pay Verizon roaming fees, hence the company is trying to expand and fix it's network.
Yes, your phone will have Sprint bloat on it.
Funny thing is that customers pay Verizon a lot of money each month. I hardly ever call anyone, but send lots of text messages. I think Verizon plans are expensive for people who predominantly text. If I want fast speeds I'm on WiFi at home where I get up to 100 mbps download speeds with Xfinity.