That is one interpretation.
I do not find it has any merit.
It does not conform with the harmony of the Quran, nor does it reflect the character of Mohammad.
The traditional understanding is thus.
Existing Peace Treaties remained valid until the End of Their Term
This is an exception regulating the longest extent of time for those who have a general treaty - with out time mentioned - to four months.
They would have four months to travel the lands in search of sanctuary for themselves wherever they wish. Those whose treaty mentioned a specifec limited term, then the longest it would extend was to the point of its agreed upon termination date.
Hadiths in this regard preceeded. So anyone who had a treaty with Allah's Messenger , it lasted until its specific termination date. However, those in this category were required to refrain from breaking the terms of the agreement with Muslims and from helping non-Muslims against Muslims. This is the type whose peace agreement with Muslims was carried out to its end. Allah encouraged honoring such peace treaties, saying,
(Surely, Allah loves those who have Taqwa) ﴿9:4﴾, who keep their promises.)
(5. So when the Sacred Months have passed, then fight the Mushrikin wherever you find them, and capture them and besiege them, and lie in wait for them in each and every ambush.
But if they repent and perform the Salah, and give the Zakah, then leave their way free. Verily, Allah is Oft-Forgiving, Most Merciful.)
This is the Ayah of the Sword
Mujahid, `Amr bin Shu`ayb, Muhammad bin Ishaq, Qatadah, As-Suddi and `Abdur-Rahman bin Zayd bin Aslam said that the four months mentioned in this Ayah are the four-month grace period mentioned in the earlier Ayah,
(So travel freely for four months throughout the land.) Allah said next,
(So when the Sacred Months have passed...), meaning, `Upon the end of the four months during which We prohibited you from fighting the idolators, and which is the grace period We gave them, then fight and kill the idolators wherever you may find them.' Allah's statement next,
(then fight the Mushrikin wherever you find them), means, on the earth in general, except for the Sacred Area, for Allah said,
(And fight not with them at Al-Masjid Al-Haram, unless they fight you there. But if they attack you, then fight them. )﴿2:191﴾ Allah said here,
(and capture them), executing some and keeping some as prisoners,
(and besiege them, and lie in wait for them in each and every ambush), do not wait until you find them. Rather, seek and besiege them in their areas and forts, gather intelligence about them in the various roads and fairways so that what is made wide looks ever smaller to them. This way, they will have no choice, but to die or embrace Islam,
Who performs Salah, and gives Zakah?
Only muslims
Conforming with the harmony of the Quran.
8:39
And fight them until there is no more Fitnah (disbelief and polytheism: i.e. worshipping others besides Allâh) and the religion (worship) will all be for Allâh Alone [in the whole of the world[]]. But if they cease (worshipping others besides Allâh), then certainly, Allâh is All-Seer of what they do
2:193.
And fight them until there is no more Fitnah (disbelief and worshipping of others along with Allâh) and (all and every kind of) worship is for Allâh (Alone).[] But if they cease, let there be no transgression except against Az-Zâlimûn (the polytheists, and wrong-doers, etc193
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