In the US, they're usually not. The coupon payments from bonds underlying the ETF are usually paid out as distributions to investors. Investopedia's article on bond ETFs, as well as this ETF FAQ state that many bond ETF's pay coupon payments out as distributions on a monthly basis (quoted portion is from Investopedia):
Bond ETFs pay out interest through a monthly dividend, while any capital gains are paid out through an annual dividend.
ETF distributions aren't normally reinvested in the underlying fund automatically because this would incur additional commissions.
Some brokers offer an option to reinvest distributions, but the availability of this option depends on the broker, not the fund, so you won't find information about it in the prospectus. For example, Vanguard states on their ETF information page that investors looking to reinvest distributions from Vanguard ETF's should ask their brokerage firm if this is an option. iShares UK and Vanguard Canada also state that for individual investors, distribution reinvestment varies on a per-broker basis.