I think an alt 1848 analogue with a surviving HRE could either try to reform it or destroy it, depending on how the reigning Emperor reacts to their revolution.
Providing a PoD at or after the French Revolution, the Reigning Emperor is going to be an Austrian. If the PoD leads to a less Reactionary Hapsburg Emperor, which is extremely likely in my estimation as a surviving HRE suggests that Napoleon's Conquests were either vastly less or prevented outright, then they might be more willing to work with the Revolutionaries. Technically, even in our Time Line the Austrians did issue a constitution, they just later rescinded it.
A Surviving HRE's biggest impact would likely be that the Revolutionaries will look more favorably on a Multi-National State, thus they wouldn't mind the Austrians ruling over Hungary as well. Historically the Multi-National nature of the Austrian Empire was what prompted the German Revolutionaries to try for Prussia, in this scenario there's every reason to try for Austria, and no real incentive for Prussia except possibly from hard-line Protestants. But even then, Austria has ruled a relatively religiously free HRE for a while now, so moderates will probably be cool with Austria provided their religious freedom is preserved, which will probably be written into the new HRE Constitution.
Of Course, all of this is dependent on how the Ruling Emperor and the Electors handle the Revolutionaries. If the Emperor opposes them outright, and all of the electors do too, then they might radicalize and decide to go for a Germany Instead.