A standard monetarist answer to his question would be "yes." But in my experience the connection between M2 and inflation can be quite convoluted, to say the least. Let me explain this by first noting that the connection between M2 money growth (M2 being the most reliable, enduring and meaningful measure of "money" that I'm aware of) and inflation is not always what one would expect. Milton Friedman was one of the best economists of the past century, but his inflation forecasts over the past three decades, based on his observations of M2 growth, were often famously off the mark. Here are two charts which illustrate the difficulty of relating M2 growth to inflation.
In the first chart I show the 2-year annualized growth rate of M2, with an overlay of different colors which depict periods of rising and falling inflation. I use the 2-year growth rate of M2 to smooth out the monthly fluctations and focus on the trend, and also to recognize that there is a lag between money growth and inflation. If money growth is high for one year and then low the next, it's impact on inflation is not going to be as big as if it is high for two years. In the second chart I present the history of consumer price inflation on a rolling 12-month basis, in order to back up my choice of rising and falling inflation periods in the first chart.
There are quite a few conundrums that jump out of the first chart. First, M2 growth in the 1970s was about the same as it was in the early 1980s (about 9% a year on average), yet inflation rose sharply in the 70s and fell sharply in the first half of the 80s. Inflation then rose in the second half of the 80s, even though money growth slowed down throughout the period. The early 90s is a difficult period to deconstruct, due to the impact of FIRREA on the banking system, but it does appear that faster money growth through most of the 90-2003 period corresponded to falling inflation. Finally, we see relatively slow money growth from mid-2003 through mid-2008, yet inflation accelerated.
If a novice were to draw conclusions from this, he or she might say that slow money growth leads to rising inflation, and fast money growth leads to falling inflation. That would of course run directly counter to everything that Milton Friedman taught us, when he asserted time and again that "inflation is always and everywhere a monetary phenomenon."
The source of the problem/conundrum here is that while M2 is an excellent measure of liquid money that is available to be spent, it is a much better of money demand than it is of money supply. According to the monetary theory of inflation, inflation occurs when the supply of money exceeds the demand for it; in other words, when the Fed supplies more money to the economy than the economy wants. (The Fed supplies currency and bank reserves to the system, but that doesn't mean the Fed can control the amount of M2. In the past year the Fed has poured $1 trillion of reserves into the banking system, but the increase in M2 has been comparatively very small, because banks have tightened their lending standards, and many corporations and individuals have been deleveraging their balance sheets.) If the demand for money is rising, the Fed can accommodate this—by allowing money growth to rise—without faster money growth being inflationary. Conversely, if money demand is falling but the Fed fails to offset this by tightening policy (the situation we find ourselves in today), then money growth can slow and inflation can rise.
The key to figuring out whether Federal Reserve monetary policy is inflationary or not lies in determining whether the Fed is oversupplying money or not. But you can't tell this by looking at M2 growth. One of the key insights of supply-side economics is that free markets are excellent sources of real-time indicators that can be used to tell, for example, whether monetary policy is inflationary or not. It's rather simple: if there are too many dollars in the system, then we would expect to see some or preferably all of the following: a) the value of the dollar falling relative to other currencies, b) gold prices rising, c) commodity prices rising, d) the yield curve steep or steepening, e) credit spreads tightening (since easy money is great for debtors and should reduce default risk), f) inflation expectations as embodied in TIPS prices rising, and g) currency growth falling (currency becomes a hot potato when inflation rises, so the demand for currency should fall). All of these are symptomatic of a situation in which the supply of money exceeds the market's demand for money.
(The late Jude Wanniski was by far the most prolific supply-side writer, and he wrote extensively on this subject. A vast archive of his writings can be found here.)
Since we have been seeing most or all of these rising inflation symptoms for the past year or so, that's why most supply-siders have been predicting rising inflation even though M2 growth has slowed down rather remarkably (M2 growth is essentially zero over the past six months).
Caveat: this is a highly contentious issue about which reasonable men can and do disagree.