Short answer is no. Long answer is maybe.
You can already load textures at runtime. To use additional textures in an effect there are two parts in webgl. On the shader side just add another sampler uniform.
To make it reference a texture you need to select a texture unit, bind a texture, and finally bind the shader program and set the sampler uniform to the texture unit index you’re using.
Construct’s renderer doesn’t use too many texture units so you could use an unused one to bind a texture to. To do that all you need is to get the webgl context.
The part I’m iffy about is setting the uniform on the shader. To do that you need the shader program for that shader. And that’s something that construct keeps track of. Possibly could be other ways to get the shader handle.
Anyways that’s just a general outline for how it could be done for webgl. Construct doesn’t provide anything to help with that nor does it do much to prevent that.