Answered by Mufti Mohammed Tosir Miah
Question:
Is 40 days Tabligh derived from the Quran or Hadith
Answer:
It is not clearly mentioned in the Holy Quran that one should go for 40 days Tabligh. However, 40 days holds a significant importance in our Deen, in terms of it being a number which builds about a change in a person.
For example, in the Holy Quran Allah 
said:
“We appointed 40-nights for Musa.” (Surah Baqarah v.51)
Furthermore, it is mentioned in a hadith narrated by Saaiduna Anas Bin Malik 
“Whoever prays to Allah for forty-days in congregation, reaching the opening Takbeer, will have immunity from two things: freedom from the Fire and freedom from hypocrisy.” (Sunan Tirmizi)
Regarding your second part of the question, spending time for Tabligh, just purely looking at it from a literal point of view will be considered as “fee-sabeelillah”
Imam Bukhari 
has mentioned a hadith that who so ever goes in the path of Allah (fee-sabeelillah) and dust gathers on their feet, then Allah will forbid the fire of Hell on them. (Sahih Bukhari p.124 v.1)
In this hadith Imam Bukhari has included the going towards the Jummah prayer as “fee-sabeelillah” (Inaamul Bari p.79 v.4)
From this we can derive that any travelling with the intention to gain nearness to Allah like seeking knowledge, purely from a literal point of view it will be considered as “fee-sabeelillah”.
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham