You are probably going to have to deal with a good amount of false positives, particularly if your code base is large.
Most static analysis tools work using "intra-procedural analysis", which means that they consider each procedure in isolation, as opposed to "whole-program analysis" which considers the entire program.
They typically use "intra-procedural" analysis because "whole-program analysis" has to consider many paths through a program that won't actually ever happen in practice, and thus can often generate false positive results.
Intra-procedural analysis eliminates those problems by just focusing on a single procedure. In order to work, however, they usually need to introduce an "annotation language" that you use to describe meta-data for procedure arguments, return types, and object fields. For C++ those things are usually implemented via macros that you decorate things with. The annotations then describe things like "this field is never null", "this string buffer is guarded by this integer value", "this field can only be accessed by the thread labeled 'background'", etc.
The analysis tool will then take the annotations you supply and verify that the code you wrote actually conforms to the annotations. For example, if you could potentially pass a null off to something that is marked as not null, it will flag an error.
In the absence of annotations, the tool needs to assume the worst, and so will report a lot of errors that aren't really errors.
Since it appears you are not using such a tool already, you should assume you are going to have to spend a considerably amount of time annotating your code to get rid of all the false positives that will initially be reported. I would run the tool initially, and count the number of errors. That should give you an estimate of how much time you will need to adopt it in your code base.
Wether or not the tool is worth it depends on your organization. What are the kinds of bugs you are bit by the most? Are they buffer overrun bugs? Are they null-dereference or memory-leak bugs? Are they threading issues? Are they "oops we didn't consider that scenario", or "we didn't test a Chineese version of our product running on a Lithuanian version of Windows 98?".
Once you figure out what the issues are, then you should know if it's worth the effort.
The tool will probably help with buffer overflow, null dereference, and memory leak bugs. There's a chance that it may help with threading bugs if it has support for "thread coloring", "effects", or "permissions" analysis. However, those types of analysis are pretty cutting-edge, and have HUGE notational burdens, so they do come with some expense. The tool probably won't help with any other type of bugs.
So, it really depends on what kind of software you write, and what kind of bugs you run into most frequently.