There are many possibilities. THe most likely, in my estimation, is that the Hilonim will choose to tolerate Israel becoming increasing frum and re-focus their efforts on preserving the rights of the hiloni (which include non-Jewish no-Arab goyim) to autonomy (they can have their own secular institutions but not impose their will on society as a whole). In that scenario, the army would not attempt to draft hareidim (or anyone else), but rely on inducements to enlist (such as meaningful accomodation of halacha in all units, money, etc.). Remember that there will soon be, and perhaps already is, a Shomer Shabbos majority – and certainly there is so if you only count Jews. Also the gap between Religious Zionists and Hareidim has shrunk – they learn the same Torah, often in the same institutions, agree on most issues (at least compared to the hiloni elites) and both increasingly hate the Israeli ruling class.
The other possibilities are traumatic. One is that Israel will so weaken itself that it will collapse. Another possibility is that once Orthodox Jews take over, they may find it easier to deal with the Muslims than with the Hilonim We would insist on keeping an army but perhaps being less “in your face” about it, and on Jews being able to live anywhere they want – but would accept Islam replacing western Euro-American culture as the dominant force in society – frum Jews of all flavor really want to be able to live in peace as frum Jews in Eretz Yisrael but don’t attach importance to being able to rule over the goyim or do things like force abortion, gay rights, etc. on them. The Muslims who lost property would get paid off, and the country would be a large Islamic Arab state albeit with a well armed Jewish minority. Muslims really hate be rules by non-Muslims, but the rest is negotiable.
Then of course, Israel will keep fighting, increasingly weakened, and will end up being wiped out militarily. Note the increasing movement in many western countries to object to bris milah and kashruth – this is a cover for renewed anti-semitism. The zionists should not expect help from abroad.