If by Follow-up you mean activities that extend to after product is released to production, or installed in a production system where QA has access (such as web sites) then I'd say yes. There are Acceptance Tests, Customer Tests, Post Mortems and other Verifications that can be performed once product is released.
Well it depends on what you are doing in QA. Taking a definition from wikipedia:
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Quality assurance, or QA for short, is the set of planned and systematic actions necessary to provide appropriate confidence that a product or service will satisfy the requirements for quality.
Quality Assurance is a wide rage concept concerning all the matters collectively or individually, which directly affect the quality of product. It control's quality of product by doing in process quality check's. So it is a brain of organisation.
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If your work is all about generating process and procedures then you should be making sure that they are followed, if as QA you are writing and exectuting tests, then maybe not. If its the latter then its probably a management task, which is where it was handed in some of the companies that I have been in; so that Engineering Managers made sure people followed the particular process their part of the lifecycle required.
Typically there are coiple of types of groups within organizations. One is QA and the other is a process improvement group, sometimes called SEPG, PEG, or whatever. The QA may 'follow-up' in terms of ensuring required reviews are conducted, sign-off's obtained, appropriate templates and checklists are used,etc. The process group may follow-up to facilitate the use and understanding of these process assets and also work with QA to improve process effectivenes.
That may occur in larger companies, but not all, the places I have worked for QA has fulfilled both roles with testing and putting processes in place. If a place has both groups great it allows for more focus, but "typical" is pretty general.