Vulkan GLSL has some additions to OpenGL GLSL.
For example, in Vulkan GLSL there is the push_constant layout qualifier, which does not exist in OpenGL.
layout( push_constant ) uniform BlockName
{
vec4 data;
} instanceName;
Another example is descriptor set bindings. Also don't exist in OpenGL:
layout(set = 0, binding = 0) uniform BlockName
{
vec4 data;
} instanceName;
My question is: considering this is GLSL code (even if it's Vulkan-flavoured), would that code compile in OpenGL? Maybe the OpenGL compiler can ignore those layout qualifiers as long as the #version is something recent enough that Vulkan has been considered in the GLSL spec?
No.
In the GLSL 4.6 spec, you will find both references to OpenGL and Vulkan.
OpenGL-flavoured GLSL won't compile in Vulkan. This one is more obvious, since in Vulkan you are required, for example, to specify either a set-binding pair or push_constant qualifiers for uniforms, and that concept doesn't exist in OpenGL. So those qualifiers would be missing, and thus won't compile.
To answer the actual question:
Vulkan-flavoured GLSL won't compile in OpenGL either.
In the GLSL 4.6 spec you will find the following paragraphs. They explicitly mention that those two cases mentioned in your question should NOT compile.
About push constants (4.4.3):
When targeting Vulkan, the push_constant qualifier is used to declare an entire block, and represents a set of push constants, as defined by the Vulkan API. It is a compile-time error to apply this to anything other than a uniform block declaration, or when not targeting Vulkan.
About descriptor sets (4.4.5):
The set qualifier is only available when targeting Vulkan. It specifies the descriptor set this object belongs to. It is a compile-time error to apply set to a standalone qualifier, to a member of a block, or when not targeting an API that supports descriptor sets.