Basically, no, although it's hard to say for sure. Most animals fear fire and will avoid it: only some of the more intelligent birds and primates seem to have learned that fire can have some benefits, too.
The animals in the scene of the burning tree are mostly owls, reptiles and arthropods (spiders, insects etc). The latter, in particular, will generally avoid fire because they dislike smoke: witness how a campfire is often used to keep bugs away. Lizards are a more complex case and there is evidence that their reaction to fire is based on learned experience, and those who have had narrow escapes from dangerous wildfires are more fearful than those who've not encountered fire.
In terms of the "truce" it's worth noting that most of the arthropods are big - "tarantulas" - and most of the reptiles are small - "little desert basilisks". While lizards certainly do eat spiders and scorpions they tend to be of the smaller variety. So the truce is really more between these venomous creatures and the kid than between the creatures themselves.
Given, then, that the scene is unlikely, what are we to make of it, presuming McCarthy invented it for a good reason? By using the dates mentioned in the novel it's possible to try and construct a timeline of the events in the plot. Since the gang left Ures on December 5th, according to this timeline, it appears that the truce of the burning tree occurred on the night before Christmas.
This chimes with the fact that there's a lot of religious symbolism in this scene. The kid is a "solitary pilgrim". The vipers are also to be found "in Babylon". The lightning of the night leaves a satanic stink of sulphur. And the fact that the kid remains unmolested by the animals is suggestive of Jesus surviving 40 days in the wilderness. The burning tree itself and the pillar of smoke it gives off are both mentioned in Exodus.
Of course, Blood Meridian is full of biblical language and allusions. But it strikes me that this is, perhaps, indicative of the way the kid is different from the rest of the gang, a little more civilized and conscionable (you may be interested in my question about this latter aspect: In Blood Meridian, why does the judge call out the kid as being different?). Later the judge - a figure who is in many ways Satanic (the scene in which he teaches the gang to make gunpowder is strongly reminiscent of a scene with Satan in Milton's Paradise Lost, for example) - will take the kid to task about this.