That said, the answer is probably "yes." Toothpaste is definitely better than nothing, because air (i.e., nothing) is a terrible heat conductor. That said, there are other properties to consider. From Wikipedia
How well it fills the gaps and conforms to the component's uneven surfaces and the heat sink
How well it adheres to those surfaces
How well it maintains its consistency over the required temperature range
How well it resists drying out or flaking over time
How well it insulates electrically
Whether it degrades with oxidation or breaks down over time
I think that toothpaste might work for the thermal part, but you might have other problems in the short- or long-run.