"Use constexpr wherever possible" -- Scott Myers, item 15, Effective modern C++

Already const is an overloaded term which means multiple things in multiple contexts. Given this, and Myers' guidance, suppose I am feeling adventurous and do a project wide search and replace of all instances of const with constexpr, what is the worst that can happen?

-- If the previous code with const was working fine with no errors, should I expect to see no errors when each instance of const is changed to constexpr on compilation?

-- Is constexpr more overloaded in its meaning than const ?

-- Can this change of all consts to constexprs lead to subtle bugs or undefined behavior even though the code compiles fine?