I can't see any features between the two that shout 'NO' to me.
The i3-3xx line shipped before any of the Pentium P6xxx.
It's a fair upgrade. P6100 = 3DMark 06 - CPU @ 1840. Core i3-380M = 3DMark 06 - CPU @ 2701.
In your place I'd look for a Toshiba Satellite support forum and look to see if any of the other Toshiba Satellite L655 owners have managed a successful P6xxx to Core i3-3xx or i5-4xx upgrade.
Intel Core i3-380M Mobile processor @ CPU World
http://www.cpu-world.com/CPUs/Core_i3/Intel-Core%20i3%20Mobile%20I3-380M%20CP80617004116AH.html
Intel Pentium Mobile P6100 @ CPU World
http://www.cpu-world.com/CPUs/Pentium_Dual-Core/Intel-Pentium%20Mobile%20P6100.html