Using wordpress to complement existing php site

I have an existing older site programmed in php with no discernable back-end making it very cumbersome to update and keep current for google. Site: https://www.fireinvent.com. As money is tight, we need to find a solution where we can work on updating for SEO without redoing the entire site (which would be preferable).

My question is – can I install wordpress to create a new front page and blog on the same domain as the existing site without creating a problem? The structure I would like to create is: //domain.com and //domain.com/blog to be in wordpress. //domain.com links directly in to the existing site, retaining existing url structure. Is this a reasonable way to solve our dilemma? If yes, what pitfalls do you foresee?

Grateful for any help as my coding savvy stops at html with ftp upload and wordpress.com.