Hello,
Yes, you can link code to requirements in EA.
What you need is to get both the code and the requirements into your model. The code can be reverse-engineered, and you can trace requirements to individual attributes and operations, although this is an EA-specific function which is in violation of the UML standard and thus unlikely to be supported in any other tool.
Pulling the requirements in from another source is also possible, but unless you're using DOORS there's no ready-made solution. If you've got them in a simple format which you can Excel-ify, you can turn that into CSV and import the requirements using EA's CSV import.
You will need to draw the relationships yourself. EA does not have a function to import code + requirements.
As to the testing side, EA has two different tracks. You can either represent your tests with model elements (there's a Test Case element, or you can use sub-typed requirements), or you can use EA's Testing facility.
The latter is geared towards actually running your tests from within EA, while the former is better if you just want to see a visual representation of your tests, trace them to your requirements and/or code, and pull some reports out of the model.
Again, there isn't much support for pulling test cases into the model from another source, but if you can get them into a CSV format you can import them that way.
You can do all the above without using SysML if you wish.
HTH,
/Uffe