Is it possible to have the laminar flow above $Re=10^7$?
The airfoil always starts with a laminar boundary layer; at some point on the airfoil surface, the boundary layer may transition to turbulent. In a uniform free-stream, two modes of transitions dominate:


Natural transition
Forced transition


a. Natural transition

Natural transition is the transition mechanism that we typically associate with Reynolds number. As flow moves along the airfoil, the local Reynolds number increases and any initial disturbances amplify. When the amplification increases past the maximum threshold that a laminar boundary layer can tolerate, the flow separates locally (laminar separation bubble) and reattaches as turbulent boundary layer.

The following graph (Ref. Drela, Flight Vehicle Aerodynamics) shows the growth of the local Reynolds number ($Re_\theta$) and the instability parameter ($\tilde{N}$) for a flat plate. Once $\tilde{N}$ increases past the critical value ($N_{crit}$), then laminar-turbulent transition occurs. Notice also how the point of transition is affected by the free-stream Reynolds number ($Re_\infty$): the higher the free-stream Reynolds number (which is what your OP is asking), the earlier the natural transition.



Image ref: Drela, Flight Vehicle Aerodynamics

Since the shape of the airfoil affects the pressure distribution, it also affects the boundary layer shape. You can modify the airfoil shape to delay the transition as much as possible in order to minimize skin friction drag. This is the design objective of Natural Laminar Flow (NLF) airfoils. But even on NLF-0215F at a $C_l$ of 0.65, for example, transition occurs at 61% chord on the upper surface, at a free-stream Reynolds number of 5 million.

b. Forced transition

Forced transition occurs when there is irregularity or protuberance on the airfoil surface. This can be due to manufacturing tolerances, contamination, or by design. Contamination can be due to rain, ice-buildup or even collision with insects. 

Thus in practice, actual transition would occur much earlier than predicted via natural transition.