Snowball sampling involves the potential for arbitrarily long reference chains (I contact Alice, who gets me in touch with Bob, who gets me in touch with Chris...) so this isn't that.
If you've already started sampling, changing methodology mid-sample is probably a bad idea. File this under things to think about next time you design a sample, and please remember to talk to a statistician before running a sample.
If you haven't started sampling, then yes, you absolutely should collect this extra info, but you need to factor selection probabilities into how you analyse the data. Full discussion is beyond what can reasonably fit in a SE post, but the basic idea is that you need to know the selection probability for each unit (e.g. AED) and then weight accordingly to these selection probabilities.
For example, let's say my sampling frame encompasses 1000 small businesses which each own one AED, and 100 large businesses which each own 10 AEDs. (Total: 2000 AEDs, 1000 owned by small businesses and 1000 by large businesses.)
Let's assume that you're trying to estimate what proportion of AEDs have been used in the last year, and let's suppose that there's a systematic difference between small and large businesses: all of the large-business AEDs are used every year, and none of the small-business ones.
(Obviously this is unrealistic, but an exaggerated example makes the issues easier to see.)
Now suppose I run my survey by randomly selecting an AED from my list of 2000, ringing up the business that owns it, and asking about all their AEDs. Since 50% of the AEDs are owned by small businesses and 50% by large businesses, every random selection has a 50% chance of getting me info about one small-business AED, and a 50% chance of getting me info about ten large-business AEDs.
If I do this 100 times, I can expect to end up getting data on about 50 small-business AEDs and 500 large-business AEDs. Even though only 50% of the AEDs out there have been used in the last year, 500/550 in my sample have been used, so a naïve analysis will grossly overestimate usage of AEDs.
The solution to this is to weight by selection probability. In this case, each small-business AED has a 1/2000 chance of showing up on each 'draw', and each large-business AED has a 1/200 chance of showing up. Hence, when I'm analysing my data, I should weight the small-business AEDs 10x as heavily as the large-business AEDs.
If you're trying to estimate things like standard errors from your data, then it gets a bit more complex, and you really ought to talk to your friendly neighbourhood statistician.