Do sound characteristics matter when moving from midfi to hifi?

Hypothetically, if going from Sony, Marantz, Schiit am I going to find something that I don’t like about Pass Labs, Conrad Johnson, Coda?

Oh hell yes. :)

I think that our industry pushes you to upgrade based on perceived value ($$$) instead of your hearing. 

Instead of asking yourself what is better according to  some rag, go out and listen and ask "what is this sound worth to me?" You end up with a better balanced view of not just what the value of equipment is but who YOU are as a listener and what YOU enjoy.  Of course I have my brand darlings, but they are MY darlings.  If you hear them and you don't like them, what difference does it make to you what I like, recommend or have waxed romantic about here? Same for reviews and the brand machines out there. 

Audiophiles who have given up upgrading for the sake of upgrading and have realized what they like and what sounds good for themselves end up happier and wealthy. :)

You can absolutely upgrade from midfi to hifi tier and not like the result. There are matters of synergy and taste at play. Look at the used market! Lots of high end gear getting constantly shuffled around. Lots of mid and low tier gear too, and some of those sellers may be trying to reach for the next tier for satisfaction :)

However, higher tier components get to remove budget constraints in their design and implementation. This allows changes that matter....and some that probably don’t (cosmetics). But IF it was engineered well and voiced right and synergizes well with your system...it can be magic. If you get one of these components to elevate your system, it will probably hype you up to go buy more high-tier components...which you may experience mixed results with :P

There is truth in all of the above posts. There is singular path on this journey, there will likely be regressive, lateral and hopefully progressive moves, I've certainly experienced this. For me its been a long slow journey, I began by listening to lots of live concerts and audio systems at dealers and shows, In doing this I developed a reference for preferred presentation and how hifi differed from live sound, this not a planned thing, really didn't know a thing about high end audio at this point. Alongside this purchases of equipment, started off relatively low end, progressed through mid grade and on. Having heard my references for high end audio early in the game, and of course new ones continually popped up I only knew my own system wasn't up to the task which drove me to continually upgrade to the point where I now have the system I always strove to have. This was a decades long journey for me, I suppose today's audiophiles have it easier in some ways, harder in others. Easier in that so much knowledge to be gained via interwebs, harder in that who knows what info is good or applies to my situation and many fewer dealers, I spent a lot of time, learned a lot from dealers and reps at shows.

As for addressing your specific question, generally we're reaching for ever greater resolution/transparency in our systems, as others have mentioned this is likely to uncover weak link elsewhere which in turn means addressing that weak link, and this can go on and on. Recently I saw a youtube video from some audio show where a panel of 'experts' questioned the audience about their efforts to attain ever higher levels of resolution/transparency and their level of happiness with the results. Most raised their hands when asked if they were frustrated/unhappy with their present situation. What this says may seem pretty disheartening to many, I'll just say don't expect it to be easy, I've been pretty OCD over the years. On the other hand, who can say, every person unique, contentment may be found far more easily for some than others.

Meant to say NO singular path.

I agree that changing a single component in a system may, although not necessarily, noticeably alter the sound. For my first post-college system, I visited stereo stores in Anchorage. (During the pipeline construction years, lots of folks had some extra bucks, and there were several audio stores.) I couldn’t afford what I really wanted, but bought a Garrard turntable, an Onkyo receiver, and ADS 710L speakers. Being a buy-and-hold kind of guy, only several years later did I swap out the Onkyo for an Adcom integrated. The improvement was significant. More than several years later and after adding a Sony ES disc player, I traded the ADS speakers for Harbeth M30s (which I still use daily). Again, great improvement. Then I traded the Adcom for a Classe, even better yet. Then the Classe went kaput, and I bought a wyred4sound integrated, which I think is the best so far.

Now, I heard improvements but my choices haven’t been true high-end. But they have given my wife and I decades of pleasure. And I’ve enjoyed the process of making changes when I have. My hearing has diminished, and I don’t know whether my approach would give satisfactory results, given higher costs for audio equipment, especially speakers, which in theory are due for an upgrade.