I just want to know if a havan/homam can be performed without sankalp/sankalpam
I have found some references in this Youtube Video (Sankalpa Vidhi), which talks about why one should always perform Sankalpa before embarking upon any Hindu ritual. It also explains a Vidhi (method) of performing Sankalpa.
In this video, we find slokas (which are supposedly) from Manu Smriti, Markandeya Purana which explain that full results of the rituals are not obtained if Sankalpa is not uttered.
Sankalpena vina karma yatkinchit kurute narah |
Phalam chapyalpakama tasya dharmasyarcha kshayo bhavet || (Manu)
Sankalpa muloh kamah vai yajnah sankalpa sambabhah |
Vritani yajna dharmashcha sarve sankalpajnah smritah || (Markandeya Purana)
Translation as per the narrator/author is roughly "If any Karma is performed without uttering Sankalpa, then the full fruits are not obtained, some fruits are lost and half of them are obtained".
Another verse is also quoted, which specifically talks about performing Yajna/Homa:
Masa paksha tithinashcha nimittanam cha sarvashah |
Ullekhanam na kurvano na tasya phala bhagabhavet ||
If before performing the Yajna, month, Tithi, Nakshtra etc. and the purpose are not mentioned in the Sankalpa, then the fruits of the Yajna are not obtained.
So, it is always wise to utter Sankalpa before doing the Yajna.