TL;DR: Sure, maybe, why not? We don't have any first-hand accounts of pagan warriors from the period to corroborate it or to suggest that they weren't thinking "fuck it, if I die it's babes and booze and blades 'til the world's ending!"

Ooof, this is an interesting and difficult (if not impossible) question to answer for a couple of reasons.

First, we have no contemporary literary evidence from warriors or practitioners of the religion to give us any sort of basis for saying "well, if I die gloriously in battle, to Valhöll or Fólkvangr I go, so who cares!" During the time these would have been active religious beliefs. There are poems, like Eíriksmál, which show the traditional image of Valhöll awaiting gloriously dead warriors, but they're praise-poetry and of course the subjects are fearless and bold and die heroically and gloriously and without a second thought.

Runestones don't really help with the psychological end of things either, since the majority of them are Christian (approximately 50% of the ones in Scandinavia, and over 70% in Uppland, Sweden.) Those which are pre-conversion don't mention Valhöll explicitly, either. The closest we have are depictions of Ragnarök like those on the Ledberg stone and in carvings like the Tjängvide stone.

There are valkyrie references on the U1163 stone, with an image of Sigrdrífa giving Sigurð a drinking horn, and the Rök stone references Gunnr while the Karlevi stone refers to Þúðr. That the valkyrjur are present does suggest that there is a prevalent belief in Valhöll that matches the later, post-conversion idea of it being a place where the chosen slain arrive after battle.

That said, you still need to be chosen to go to Valhöll, and the way you get picked is to be the second string of warriors, since Freyja gets first pick of the day's dead for her hall in Fólkvangr. There's a lot to be read into about that, with references in Grímnismál 14

Fólkvangr er inn níundi,

en þar Freyja ræðr

sessa kostum í sal;

hálfan val

hún kýss hverjan dag,

en hálfan Óðinn á.

Fólkvangr is the ninth And there Freyja rules She chooses the seats in the hall; Half the dead She choses each day And half to Óðinn go.

and Skáldskaparmál 20:

...eigandi valfalls ok Sessrúmnis ok fressa

possessor of the slain and Sessrúmnir and tom-cats/bears.

and Ursula Dronke's suggestion in her edition of the Elder Edda that Freyja got first pick because, while Óðinn could kill everyone he wanted, she could restore life to them, and thus would have basically had infinite forces available to her in the war between the Æsir and Vanir.

It seems to me, at least, that if you're looking to "win" at dying well, you want to be the one picked by Freyja, as she's going to pick the cream of the crop.

So what does this mean for your question about them being fearless on the battlefield and excited for war? We don't know, simply, and it would certainly vary from warrior to warrior. Culturally, there was absolutely an expectation of martial practice and valour among the warrior-elite, and that would weigh on the minds of that class. There is nothing to suggest that they were stone-cold killers one and all, eager and chomping at the bit to go into battle and die gloriously for Valhalla awaits, but at the same time it is possible - or maybe even likely - that there were pagans who felt that the promise of an almost-eternity of feasting and fighting made them fanatically sure of their actions in battle and thus essentially fearless and eager for warfare. That said, though, we do know that there were certainly times when pagan vikings were routed, as in Seville in 844, Englefield in 870, Ashdown in 871, Eddington in 878, Duisburg in 884, and Brunanburh in 937, so they weren't, as a whole, utterly unshakable.