The short answer is yes.
The ultra-Orthodox are Israel's fastest growing demographic. At the moment, secular and moderatrely religious Israelis are the majority (I count secular/moderately religious Israeli-Arabs as part of this too, not just secular/moderate Jews), but this is changing in favour of the ultra-Orthodox due to their much higher birth rate.
The ultra-Orthodox already form a religious voting block that vote for political parties such as Shas and others, who seek to impose more Jewish laws in Israel, increase the religiousness of the education system, increase funding for religious institutions (naturally using taxpayer money from the secular/moderate majority) and generally gradually turn the country into a theocratic Jewish state. Many religiously Zionist "modern Orthodox" voters vote for different parties that do similar things in terms of religious education and laws.
Benjamin Netanyahu is Prime Minister and is of the secular right-wing Likud party, but the religious voting block is already large enough that he is forced to form a coalition government with them in order to stay in power, so already the religious parties have a high degree of influence in government decisions. Consequently, the democratic decision to conscript Haredim into the IDF and stop giving them special treatment was reversed, despite the wishes of the majority of the population.
My family is secular and somewhat patriotic, but already we have seen great changes in the Israel we love and know. I have small cousins who are being effectively brainwashed with religious nationalistic propaganda at school and it is up to my uncles and aunts to explain to them at home that it's okay not to observe a leila seder or shabbat meal in the exact religious way, when we're just doing it for sentimental reasons. Another relative of mine was excited to go on a school trip to the Negev Desert to see all sorts of beautiful stuff, which has been done for years, but instead the religious Minister of Education has now decided that kids must go to Hebron instead. Why would a secular kid care about Hebron?!? And why should we normalize the occupation by sending kids into the Occupied Territories?!? It's bad enough that they'll be forced to risk their lives defending religious nutcases living in settlements in those Occupied Territories, once they reach 18.
When the ultra-Orthodox become a majority, they will vote in a religious majority government and turn Israel into a Jewish version of Iran or Saudi Arabia. It' a very worrying issue for those of us who think Israel should be a secular and free country.
The secular Jews are worried and of course the Arabs are worried. We should all be worried.