Hola Janusz

We'd have to explore lots of different sentences using these two to make sure, because sometimes the infinitivo perfecto and the gerundio compuesto are linked to modal verbs or some prepositions and they may change the function, but yes,  I think it's safe to get to that conclusion: haber tenido is going to have the function of a noun and habiendo tenido will be an adverb. The adverb can be a different type, though. For example, in your sentence:

Habiendo tenido ese accidente, depende de su pareja. 

As he had that accident... (cause = because he had that accident) 

However:

Habiendo dicho eso, se fue. 

When/once he said that, he left.  (time)

Saludos