No, that’s not a rare meaning of the word that the artist used here, but a sheer invention, for the sake of imaginative suggestion.

A very strange one, by the way.

This name make no sense in French.

The same surrealistic Chilean painter, Roberto Matta, seems to have created other œuvres named:

• « L’œuf de l’oeil »
• « L’œuf du verbe noir »

which are just as meaningless.

Roberto Matta is a surrealist painter, as well as being a poet & philosopher, and one shouldn’t always try to find an obvious meaning to the titles of his works. The round shape of the egg and/or of the eye is very frequent in Matta’s work (Ojo con los Desarrolladores, El Ojo Del Ciclón, … even when the words aren’t in the title, so there’s no reason to be surprised of finding it in the title of this particular work. The idea of the verb, of the word, is much present in his work, as in all surrealists’ works. I think the proper title of the work is “L’oeuf de verbe voir“. Can’t tell if de was wanted by Matta (he lived in France for some time and was acquainted with Breton and others and probably could speak some French) but the passage of de to du is IMHO a mistake that probably originated by someone who either wanted to “rectify” what he thought was a mistake or just made a copy error. But it is very important you look into this if you want to analyze the painting because I wouldn’t interpret “oeuf de verbe” and “oeuf du verbe” in the same way. Personally I’m in favour of “oeuf de verbe“. I’d wager on an interpretation that the painter is analyzing what is at the origin (the “egg” is an element of the birth process) of the verb. The two people on the left hand side are kissing and/or making love and we can see what looks like a heart on the middle parts of the two bodies. This might create the anger of the person on the right-hand side, anger expressed by a verb, a word, that we can imagine. When dealing with the surrealists imagination is a great help in the understanding. Other, or complementary relationship, between oeuf and verbe could be found in the Bible^*, although I don’t think Matta was religious.

Disclaimer:
This post has nothing, or very little, to do with French language, but I couldn’t make it shorter for a comment, and there’s no place on stackexchange I could refer the OP to for a beginning of an explanation of the use word oeuf here.

^* “In the beginning was the Word…”, “The Word became flesh…”
(John 1:14)