Don’t be silly, of course US dollars help their military.
Imagine talk is really not what we need here. Let's use observed dollar totals for spending and sales.
In 2015 China's total sales of foreign goods and services was about $600B more than their purchases (U.S. share = $91B). Now, that would be plenty of money to cover their $150B 2015 military budget (about half their total gov't spending) --providing they were able to pay their personnel and suppliers in Euros, pounds sterling, and dollars (Australian, U.S., Canadian, etc.) but then they couldn't pay off their foreign $600B trade deficit in their purchases of land, bonds, design rights, and buildings.
Here's what we got: China's 2015 gdp was somewhere between $12T and $20 depending on who you talk to and as we all know (I hope) $1T = $1,000B. Their government can easily sponge off their economy just like ours does. See for yourself:
https://www.census.gov/foreign-trade/balance/c5700.html
http://www.tradingeconomics.com/china/government-spending
http://www.tradingeconomics.com/china/gross-national-product