Is there any way to calculate the cumulative width of synaptic clefts?
Mathematically, you're correct to think that linearly the total distance would be sizable, however don't forget the third axis, depth.

Given the following:


  The adult human brain is estimated to contain from 100–500 trillion synapses. (Drachman D (2005). "Do we have brain to spare?".)


Let's go with 150 from your example

... and ...


  Every cubic millimeter of cerebral cortex contains roughly a billion of them. (Alonso-Nanclares L, Gonzalez-Soriano J, Rodriguez JR, DeFelipe J (September 2008). "Gender differences in human cortical synaptic density")


Let's calculate the total volume these synapses occupy:

150,000,000,000,000 / 1,000,000,000 = 150,000 cubic mm => 150 cubic cm (
You can picture this as a cuboid 15cm wide by 10cm tall which is roughly the size of a butter bar )

So if all synapses can fit in a 15cm x 10cm cuboid then the clefts could all fit in a significantly less space. 

If you want to calculate linear distance for, let's say an average of 30nm clefts then:

150,000,000,000,000,000 * 30nm = 4,500,000,000,000,000nm => 4500km