Excitability of neurons
Excitability has definitely been tested and measured, but I'm not sure about your exact definition (sort of hard to prove a negative).

For differences in "excitability" across neuron types, I can think of two general approaches.

1) You could simply consider the firing rate and define cells as more "excitable" simply if they fire more or have a lower current threshold (though one must be careful in interpreting the actual "mV" value of threshold, because resting potential and input resistance are crucial and thresholds are dynamic).

These parameters have nothing to do with the number of synapses on them or the number of synapses it takes to fire; if you focus too much on these parameters you risk making a comparison that isn't all that helpful (see the analogy below). This approach is most suited to comparisons across cell types.

2) The second type of excitability concerns the intrinsic properties of a cell: what is it's input resistance, spike threshold, how much current do you need to inject at the soma to evoke a spike, etc. These properties can indeed vary across cell types, but you really have to think about it in the context of (1) to avoid the same problems with the analogy below. A cell might be near threshold but receives very small inputs; should that cell be considered more excitable than another?

Instead, it makes more sense to think about changes of excitability: "how does Manipulation X affect the excitability of Cell K?" If it changes the amount of current you need to inject to the soma to evoke a spike by depolarizing the cell or increasing the input resistance, you would say it increases excitability. This is, in my experience, by far the primary way in which "excitability" is discussed in neuroscience, rather than as a factor that varies across neurons. I did a search on Google Scholar for "neuron excitability": every one of the first 20 results was using it in the context of a change in excitability from one condition or manipulation to another.

A tangential analogy (the problem with your proposed definition of excitability):

Your proposed definition of excitability is a bit like measuring income based on paycheck frequency or number of digits on the check. You could certainly do comparisons between jobs on those merits, and in some cases they might be valid for what you'd normally think of as "income", but as soon as you move between countries (i.e., brain regions or cell types) currency changes, and suddenly the number of digits doesn't help because you don't know if you are talking about British pounds, US dollars, or Brazilian real. And even within a population, if the paychecks come weekly rather than monthly, the same face value of a check means a totally different annual income (i.e., if a cell has synapses that are rarely active, they contribute less to depolarizing it than synapses that are active all the time).

Contributions to excitability

Your question proposes that morphology is a defining characteristic of excitability. In a previous question you asked, I directed you to a review by Magee, J. C. (2000). Dendritic integration of excitatory synaptic input. Nature reviews. Neuroscience, 1(3), 181. - this review is applicable here, too. Active conductances in the dendrites and variation of synaptic properties with distance from the soma (larger, faster EPSPs the further from the soma you go) act to regularize the influence of EPSPs with distance, so you cannot rely only on passive properties. That also means you can't simply assume that a cell with lots of synapses far from the soma is not excitable.

However, there are definitely differences in firing rates and firing thresholds across neuronal subtypes, and you can take these to mean differences in excitability. There are many papers that talk about the diversity of intrinsic properties or firing rates of cells. I'll list a couple here for further reading:

Llinás, R. R. (1988). The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function. Science, 242(4886), 1654-1664.

Izhikevich, E. M., &amp; Edelman, G. M. (2008). Large-scale model of mammalian thalamocortical systems. Proceedings of the national academy of sciences, 105(9), 3593-3598.

It's also important to recognize that excitability is dynamic and cells that are highly excitable in one state may not be as excitable in another state, even though their morphology does not change.