In general, yes. Actual studies in English are hard to come by, but here's one that actually goes in depth and shows breakdowns by age and region. Here's a more recent survey that shows a slim majority actually support increasing immigration, despite a vast majority (76%) saying that it would lead to at least somewhat more crime. Overall, though, Japan has backed itself into a situation where it's going to have to choose a path that will upset a substantial portion of the population, be that increased immigration, increased taxes or austerity. It's currently going with the middle option, but an increase in consumption tax isn't going to solve their woes.
Major in Asian Studies with a concentration on Japan, studied at a Japanese University for a year, lived and worked there for a few years, and I work in banking so I keep up on the economic news. It's one of the few subjects I can speak somewhat intelligently about for long periods of time without totally embarrassing myself. :-)