Yes, more people would travel into space if it were more affordable. Space travel and exploration has been a childhood dream for many who grew up watching NASAs' shuttle launches, and although few are accepted into an astronaut training program, many still have a fascination with the starry sky above us. Naturally, lower space travel fares would allow more of these folks to follow that dream.
What passes as current space technology has been stuck in 1960 era science. However, with the cancelation of the Space Shuttle program, the opportunity for a new era of low cost commercial space travel with practical reusable spacecraft & space planes is finally emerging.
Science has advanced a lot since 1960. No place is this more evident than in the electronic world. Transistors have replaced vacuum tubes of the 1960s providing dynamic increased functionality while enormously reducing cost. The Intel quad-core i7 CPU chip contains 1.4 billion transistors. How big would the Intel i7 microcomputer be if it was built out of 1.4 billion vacuum tubes? Larger than a football stadium? How much would it cost? Today’s ordinary smart-phone, laptops and tablets could not exist if we still used 1960 technology.
That will not be the only thing that helps space exploration though. They eventually will be able to make the rockets more efficient once they get to space. They will be able to capture the suns energy better to keep the rockets going. Could one day possibly land on the planets to pick up valuable resources, that could be used for long missions.
I personally think that lowering the cost of rocket launches will not boost the space exploration because rocket launches is far but the cost would be lower. I personally think that lowering cost of rocket launches will affect astronauts because of the boosting in space exploration and it will affect space.
I think this would just be an opportunity for the government to just give less money to agencies like NASA. We don't need to lower costs, per say, though it could help. What we need to do is allocate more funding to things like this, and then lower the cost after things are established.