As a beginning graduate student, can you do without conferences in theoretical CS? I'm beginning my graduate study in theoretical computer science soon, and I've been admitted to two graduate schools in Northeastern Asia.

One of those makes it a rule to grant compensation for travel to conferences to graduate students who finished their master's thesis.  However, for beginning graduate students, they said they cannot be sure if they can fully afford their travel costs for conferences.

The graduate school requires the students little coursework and all I will do there will be do actual research.  As you may know, conferences are important in computer science and reputable conferences are usually held far removed from us in Northeast Asia.

Can I do with journals and preprint servers, and possibly without reputable conferences, in the field of theoretical computer science, as a beginning graduate student?

(By the way, the cons of the other school are that the professor supervises too many students and that he hasn't been nice to me.)
Conferences are very important in CS. Journals are also important, but they tend to accept more mature work, and therefore might be especially hard to publish into as a beginning graduate student (which, in your terms, seems to refer to someone who hasn't finished his/her master thesis yet). Nothing is impossible, of course, but you have to be careful not to end up with no publications after 4 years, just because you were aiming too high. In addition, some journals are very slow to respond, so you might spend half a year or even more waiting for a decision. In the mean time, you cannot send this work anywhere else. 

You should ask students there how the official policy is, it might just be that they don't want to fund you a trip to a small workshop in Hawaii, but the question could be different if you were to get a paper at POPL. You should also consider that there are good conferences coming to Asia, and many conferences offer financial support to students (including reducing the registration fee, sometimes even helping with transport/accommodation). Finally, if you're writing your paper with someone else, such as your advisor, this person might be able to travel to the conference and present the paper (which would be a shame for you not to attend, but it still counts as a publication in your CV). 

EDIT Some clarification: technically speaking, the only important thing is to produce good research, and to write good paper. What you plan to do after your PhD also matters, but if you'd like to stay in Academia, you will need at some point to get a job, and you will be judged on your papers (on other aspects too, but papers are very important). Now, to answer your question: yes, you could get a job with only journal publications, as long as they are good. Is that the best strategy? Probably not. Conferences are very important because they allow you to meet other people, to be exposed to state-of-the-art research, to confront your ideas with the community, to get published within a relatively short time period, to receive more frequent feedback, to construct your research project in a more incremental way (present your idea at some workshop, work on a good conference paper, present the extended version to a journal). 

If I can give you one example, I've presented some of my work at a workshop with no proceedings (so it didn't count as a publication), and I met there someone who accepted to be one of my external PhD examiners.