Generally yes, although it depends on the type of visa the immigrant has. Typically if an investor has a B visa or if they come from a country where they're able to use ESTA, there are no problems with traveling. Sometimes we get stories of clients who are stopped at the airport and questioned, but we haven't encountered any major problems.
Traveling outside the US may become more difficult once a client's I-526 petition gets approved, so it is important to explain to them what their visa allows for, what duel intent means and what to do if they are stopped at the border.