Most definitely, because it fits the definition perfectly: a generally accepted medium of exchange
I will focus on the last 3 worlds of this line, but first a silly example. Suppose the Federal reserve prints up trillions of dollars worth of crisp, clean bills. It packs them on trucks, ships them down to Cape Canarveral, loads them onto a shuttle and blasts them into space where it escapes the Earth's orbit and sails away into the cold, black emptiness of space. Is this money? It all looks, feels and matches the legal definition of money back on Earth, but how would it effect the prices of goods and services? The obvious answer is that it wouldn't, and so the economic answer is that it isn't money. What if the Fed printed that money, but then locked it in an underground vault and held it there never intending to use it? Same answer, so when we talk about money part of the definition has to be about the accessibility of that money. On to fractional reserve banking.
Adam takes $100 and deposits it in his bank, his bank says "come back anytime and get it", then lends $90 out to Bill who deposits that $90 into a different bank. This bank also says "come back anytime and get it", and then promptly loans out $81 to Charles, and so on and so on. If you take the sum total of everyone's bank account once the process has completed there would be $1,000 totaled across them. This is where Warren Gibson gets the idea that the "money supply" must be $1,000, Tammy is a finance guy though, so he looks at the broader picture. Every dollar created after the initial deposit is an asset and a liability. When Adam's bank makes the $90 loan they create a $90 asset, but the also saddle themselves with a $90 deficit that they owe to Adam. Back to accessibility.
Can $1,000 be withdrawn from the banking system and be spent? No. If Adam withdraws his $100, then his bank has to run to Bill and demand their $90 back (assuming all deposits and loans are callable at any time), Bill runs to his bank to withdraw the $90, who has to run to Charles to get the $81. No matter how you slice it only $100 can be withdrawn from the system and then spent on goods and services, and there is no way to get the effect of $1,000 on goods and services.
This is exactly the effect that full reserve Austrians cite when they state that Fractional Reserve Banking is fraudulent, there is no way for all people in the line to effectively use their individual deposits. If some guy in the middle of the chain withdraws his $50 to spend then that immediately prevents Adam from ever accessing his full $100, while also calling in every loan made beyond that $50 deposit.
As far as empirical (anecdotal!) evidence, I think it is on the side of Tamny. Japan has a massive public debt, which has been building for a few decades now, the level of reserves held by the Japanese Central bank have exploded, and yet the only inflation seen in the immediate past was a short term blip when the sales tax increase went into effect. If M1 is money, if government bonds paying near zero are also money (which flows from the same definition as Gibson tries to use) and if inflation is due to increases in the money supply, then you can't escape the prediction that Japan should be crumbling amid hyper inflation.