This won't have any significance whatsoever. Qatar is a tiny country with a native population of around 320.000 people. It will always be at the mercy of KSA and the GCC. Neither Iran nor Turkey are capable nor willing to alter this permanent power imbalance in KSA's favor.
The only relevant party here is the US for obvious reasons. Most importantly the 2 existing US bases in Qatar. If they give a green light for a regime change or for continued pressure (that will cripple Qatar eventually - they have already been feeling the heat tremendously) to continue in order to change certain Qatari policies that those nations disagree with, this will occur. There will be no ifs here at all. Those who think so are truly deluded.
Anyway I am sure that this dispute will be solved diplomatically as eventually it is in Qatar's foremost interests not to have a hostile relationship to their neighbors and those that they share the most with on every front by far and those whose present and future they are fully connected to.
In fact Turkey (or rather Erdogan) has the most to lose here. They either stick with tiny Qatar 100% but this will alienate the 100 times bigger market which is the other GCC states let alone much of the Arab world (Egypt in particular) that has a similar stand on Qatar. It's another political own goal by Erdogan, I am afraid, which is sad as KSA and Turkey has no reason to be enemies outside of trolling on online forums and chest jumping from Arabs and Turks alike. Erdogan is incredibly naive if he thinks that hostile interference (taking one side over the other) n a internal GCC matter won't have consequences.
I think that KSA or another country should open a military base in either bankrupt Greece (which already has a lot of Arab investment), Georgia, Armenia or Cyprus. NATO opening that regional base in Kuwait and recent political developments would not be a hindrance rather the opposite. Or somewhere in Northern Iraq or Syria. Kurds would be begging for serious GCC/Arab support. There are tons of options in case of hostile acts. As I said I would consider this a very bad development as our real enemy (Mullah's) are what we should focus on but if forced to, this might be the end result.
Some of the Turkish users here on PDF are very funny on this front. Quite surreal in fact. Anyway some of their reactions should be a wakeup call for some of the Arab sheep that think that they are our very close brothers and sisters. Sure, many of them are but not such people. Such people are quite clearly anti-Arab yet they are defending an Arab country (Qatar) and people who are the exact same like people in KSA. Comical stuff. Attacking Arabs but "defending" an Arab state (Qatar) at the same time. I hope that the average Qatari realizes that the "support" that they receive is not out of love but solely geopolitical interests. Such "crisis" should once again have taught the average Arab man and woman that they should only count on each other and not create internal divisions. Sadly it seems that whatever is going on, our leaders don't understand this currently which is why Saudi Arabians and Qataris stand together despite this ongoing diplomatic crisis. Which, if you ask me, is the most important thing here.