No, if your word mark lacks distinctiveness, you can't increase it by changing the font. A word mark is a type of trademark that protects only the name/phrase itself apart from any stylisation.
Stylistic changes can, however, make a difference when applying for a figurative mark. In fact, we often advise our clients whose word marks aren't distinctive enough to add a distinct graphical element to the brand name and try to register a figurative (logo) trademark instead. Since logos are inherently more varied than text alone, this option increases the chances of successful registration - with the caveat that the protection will extend to the new logo, so if you want to go this route, you should submit a logo you will actually be using.