It actually is possible to use that board with the Arduino Web Editor if you select the "LilyPad Arduino USB" board. The problem is that SparkFun decided to make a completely different pin mapping for the LilyPad ProtoSnap Plus. That could be overcome by translating the pin mappings. For example, the pin marked 11 on the ProtoSnap would need to be referred to as pin 2 when using it as the LilyPad Arduino USB. You could write a library that did this translation for you, for example:
#define D11 2
but that translation won't apply to libraries so if the library documentation says "connect sensor to pin 2" you need to remember that 2 means the pin marked 11 on the ProtoSnap.