In a quick short answer, YES. There are many factors which are taken into account when Google applies rankings to your site. One of which is titles.
If you have a page which ranks for a certain keyword in Google and you change the title you are risking loosing that ranking.
Before making any on-site changes to your site to gain new rankings try building your off-site optimization. Try obtaining new contextual or text links from other sites to your site using the keywords you wish to rank for. You do not want to change your titles and loose everything. Your best bet would be to try to optimize your off-site factors before making any dramatic changes on site.
Of course this all depends on the current status of your website and what titles you are using now.
