Not paying VAT would require open rebellion. Not paying income tax would be easier since its widely ignored. Since the Israelis consider students and teachers to be “unemployed” (since from a zionist perspective, learning Torah is not productive work), they don’t collect income tax on their salaries. The biggest contribution of the Hareidim to the Israeli economy is the large amount of money (including money spent by foreign students) spent on financing Torah studies that comes from other countries; this will dry up since many of the foreign students are being sent by parents who won’t send them if they see escalating conflict in Israeli yeshivos.
In reality, the only “weapon” of the hareidi community would be to follow the Neturei karta option and ally with the Muslims against the zionists (this was last tried by what is now the Eidah hareidus, but it was then Agudah Yisrael, in the 1920s, and the zionists replied by shooting the frum community’s representative and warned that anyone who tried to make peace with the Arabs would be next). It would take extreme provocation to get the bulk of the Hareidim to prefer a Palestinian state, albeit with Jewish autonomy, over a zionist state (even one that persecutes Jews).