Be very careful.
I'm not a lawyer, so this isn't legal advice. For that, you need a lawyer. However . . .
If you buy a property with tenants in place, you must observe the existing lease.
So: How hard can you have rent increase to market rent? Not at all under the terms of their existing lease.
If they refuse to pay the market rent, how easily can you get them to move out? Not easy at all. They'll point to the valid lease.
You have three options:
(1) Buy and wait until the lease expires. If there's only a month or two left, that probably won't be a problem.
(2) Ask the current owner to either remove the tenants or raise the rent as one of the conditions of your purchase. Now, he can't just break the existing lease, either. But it's better to put the burden on him. He's got more incentive to do so.
(3) Buy the tenants out of the lease. See if they'll accept a few thousand dollars to voluntarily terminate early.
If the tenants are in violation of the lease, you certainly would have the right to evict them. However, that too is better done by the current owner than you.
If the seller won't deliver the property vacant and there's a lot of time left on the lease, reduce your purchase price to account for that difference. Let's say they're renting for $300 under market rent and they've got 7 months left on the lease. Reduce your purchase price by $2,100.
Check with your Realtor for more strategies.
Hope that helps.