Can I power rails with levers in Minecraft Bedrock?

Yes.

A Powered Rail can be activated by:

  • an adjacent active power component (for example, a redstone torch, a block of redstone, a daylight sensor, a lever...)
  • an adjacent powered block (strongly-powered or weakly-powered)
  • a powered redstone comparator or redstone repeater facing the powered rail
  • powered redstone dust configured to point at the powered rail

A Lever is a power component, which is used to switch circuits on or off, or to permanently power a block.