One problem you might find with your rule is that you turn Switch Away off, and then have an IF statement to check to see if it's off. That IF will always be true. You probably want ti check to see if it's ON rather than OFF, and then set it off after the IF. I think you want something more like this. You should also get in the habit of always closing your IFs with END-IFs. If there are no statements following, the END-IFs aren't strictly needed. But they keep things neat and tidy and make the rule easier to read. If anything outside of the condition follows an IF, then you absolutely need the END-IF for the rule to execute correctly.
Trigger:
Mode becomes *changed*
Actions:
IF Mode is Away THEN
On: Switch Away
ELSE-IF Mode is Day THEN
If Switch Away is On THEN
Unlock Deadbolt Mudroom Door
Off: Switch Away
END-IF
END-IF
On the virtual switch vs variable debate... I use virtual switches because I've found that they're handy to use in other rules or apps. For example, I can use a routine in Alexa to trigger a mode (i.e. "Alexa good night"), I can use an Away switch in Mode Manager to trigger a mode, or in Motion Lighting to keep a light on/off even if there's motion. I can also refer to them in other rules. You can use local variables only in the rule they are a part of, and that works fine if you don't need the information that switch carries anywhere else. There are global variables in RM also that can be used in multiple rules. Global variables cannot be used outside of RM. And, they may slow your rule down because, as I understand it, they have to call the parent RM app rather than staying local within the rule.
Of course, this is just my preference. There are many ways to skin this cat, and any of them will work fine. It just depends on what your use case is.
I used to have one gigantic rule that did absolutely everything anytime a mode changed. It was very complex and long, and editing it was not only a real hassle, it was really slow. I broke it up into one rule for each mode, and that's worked great. But for a relatively simple rule like this one, you should be fine including more than one mode, like I did in the first example I posted above.