No. Financial institutions are subject to a franchise tax under Chapter 2B of the MBT. The franchise tax is levied at a rate of .235% on a financial institution's net capital. This tax on net capital is not a net income tax. Thus, the protection of PL 86-272 does not apply to financial institutions taxed under Chapter 2B of the MBT.
Any taxpayer, other than an insurance company, has nexus with Michigan and is therefore subject to the taxes imposed by the MBT, if the taxpayer either (a) has physical presence in this state for more than one day during a tax year, or (b) the taxpayer actively solicits sales in this state and has $350,000 or more in gross receipts sourced to Michigan. MCL 208.1200. "Active Solicitation" is defined in Revenue Administrative Bulletin 2007-06.
Public Law 86-272 is a federal law that prohibits a state from imposing a net income tax on an out-of state taxpayer whose only business activity in Michigan is the solicitation of orders for sales of tangible personal property where the orders are sent outside the state for approval or rejection and are filled by shipment or delivery from a point outside the state. 15 USC 381 et seq. PL 86-272 only applies to the business income tax of the MBT.