No, because in monetary economics, the leading theory states that inflation is based on changes in the supply of money.
With providing a $1,000/month UBI to every U.S. Citizen, we aren’t changing the supply of money. We’re just redistributing money supply already in the system and economy. And this $1,000/month UBI for every U.S. citizen, would be funded by a Value-added tax and other redistributions of budgets, and budgets now made available because of the positive effects created by providing the American mass and people the purchasing power to put back into the economy, from bottom up.
The federal government even recently printed $4 trillion for the bank bailouts in its quantitative easing program, which happened with no inflation.
Now, it is likely that some companies will increase their prices in response to people having more buying power, and a VAT would also increase prices marginally. However, there will still be competition between firms that will keep prices in check. Over time, technology will continue to decrease the prices of most goods where it is allowed to do so (e.g., clothing, media, consumer electronics, etc.).
The main inflation we currently experience is in sectors where automation has not been applied due to government regulation or inapplicability – primarily housing, education, and healthcare. The real issue isn’t the $1,000/month UBI, it’s whether technology and automation will be allowed to reduce prices in different sectors.