I think in general the answer to this is No, however I do remember that there were some significant changes to Workflow between versions 5.2 and 5.3 (and the upgrade in question is from 5.2) which might have some impact on items currently in workflow. Any experience on this question would be welcome.
No - an upgrade can (and usually will need to) be performed while there are active Workflow process instances.
The changes to workflow in 5.3 do have an impact on existing workflows, but this is mostly related to the fact that in 5.3 and later versions workflow processes are Blueprinted.
In 5.2 (and earlier versions), if you wanted to use the same workflow in several publications, you had to upload it from Visio into each publication separately. You also had to localize a schema to associate it with the workflow in the required publications. In 5.3 (and later) you just upload it once to the schema publication, associate it with that schema and it is blueprinted down into all child publications.
You have the option to enable/disable the blueprinting of the associations with schemas/structure groups on a Publication by Publication basis in the Publication properties Workflow tab (Enable Workflow Process Associations in Shared Schemas and Structure Groups checkbox) - this is unchecked by default (associations are not Blueprinted).
When upgrading, if there is a process with the same name as a process in a BP parent publication, the process will be made a local copy of the (now Blueprinted) parent process. There can be an issue when more than one parent has a parent process with the same name, in which case some renaming of processes may be required.