I take it that what you want is to determine the number of technical applications that relate to your Service Offerings, @Mark Johnson without CT allocating fractions of the amount.
FIRST IDEA:
You could replicate the allocation lines without the weighting you're using today. You'd end up with a much higher number in the Business Services object, but each entry would reflect how many relationships there are to a single Tech App. This way, you could enter your condition.
One issue I can see is that you have a 2-level allocation step between Tech Apps & Business Services. You'll end up with an exceedingly large number, if you count 1 at every level, and there are 1:n relationships on both steps.
SECOND IDEA:
I thought some more about your issue and there might be a more elegant way of doing this, without changing the allocation lines. It involves creating a second metric, with its driver at the Business Applications object. Its logic (formula) could be something like:
=If(Cost YTD!=0 AND Modeled Count>0,1,0)
Again, I need to test this, but it feels like the best approach.

It's not exactly your scenario (Vendor = 1), but it would be equivalent (logically). See that for each one of the Application / Service Offering pairs, the system counts 1 instance.
This is how I did it:

I created a new Total Count Test driver and activated the metric to go up to Business Services:

(It also works with Cost YTD!=0).
I'll write a blog post with more details after I finish my trials.
P.S. We are using your approach to count the number of servers up the model, so we can see how many there are per Business Service. The standard allocation works fine for us.
#CostingStandard(CT-Foundation)