The answer to your specific question is YES, colonial choanoflagellates are multicellular life.

But, as is common in science, there is a further question to be answered. Are colonial choanoflagellates animals?

This question depends upon what you mean by an animal. In biological terms, animals represent a coherent and evolutionarily related group.

In this circular phylogenetic tree, living organisms are at the periphery; time goes backward into the past as we move toward the center.

For colonial choanoflagellates to be considered animals, they would have to share a common ancestor with the animals and this ancestor would had to have occurred later in time than the common ancestor shared by unicellular choanoflagellates and animals.

This would imply that colonial choanoflagellates represent an evolutionary step towards the animals.

In this light, it is worth noting that colonial lifestyles have arisen independently (from unicellular precursors) a number of times, but these represent interesting evolutionary events (see Michod, 2007), not directly related to the origins of animals.

In this (hypothetical) phylogenetic tree, colonial choanoflagellates share a older common ancestor with unicellular choanoflagellates than they do with animals, so they would not be considered animals (biologically) even though they do some of the things animals do.

In the modern world, who shared a more recent ancestor with whom is generally determined through molecular level comparisons of genes and genomes.

For example, here is a molecular study (Hean et al 2007), that suggests that sponges and animals share a common ancestor.