This isn't exactly the answer you wanted and is sort of ruthless:

One guess (which is very likely to be off because of lack of context) is that the person(s) who told you to run a fellowship, told you to do this as a way of resolving a problem of not getting funding, and assumed that you >80% resolved to continue. 

This is because a fellowship would allow funders to observe inputs and outputs better and know the potential organizer better. 

So I'm saying, maybe they viewed successful execution of a fellowship as a potential signal. For example, an organizer could express certain kinds of skill or connections (that is unknowable because the people making decisions are far away). At the same time, the absence of this success, or some other lack of promise for a fellowship (which most of the time doesn't mean a lack of ability or that someone is a "bad EA"), would prevent a potential organizer from using this signal to show ability. So a fellowship is a filter.

So, I'm basically saying the "fellowship answer" might have been an answer to a specific situation of someone not getting funding, and giving them a potential path to continue. 

This answer you are reading might be beneficial, because it points out this advice might be very different than an "instruction" or "robustly good advice with guaranteed reward".

It depends on what you want virtual programs to accomplish.

In my opinion, one of the most important reasons to run these events is so the organizers can get a sense of who are the people you can support best and how to support them.

If you are already have a process in place for meeting people one and one, and you feel these are enough to give you a sense of the people in your group, you might not need your own intro program.

Also, I am not completely informed, but my impression is that the virtual programs have a low bar for admitting new facilitators (I think they might invite anyone who has completed an in depth intro fellowship? And I don´t think there are any mechanisms yet like paired facilitating to give feedback to the facilitators). So quality assurance is more of an issue - you can get a great facilitator and cohort or a mediocre experience based on luck. A local version has more control over who facilitates and the experience, if this is something you want to invest into.

Lastly, a local program can help create ties between geographically proximate members, which can lead to them meeting in person and have more interactions.

These are all pro tanto reasons. In my opinion the first one is most crucial - if you already have a process in place to meet people and get a sense of them that is probably good enough, and you can instead focusing on supporting each individual after the intro program, helping them progress in their careers, etc.

I'd add another benefit that I've not seen in the other answers: deciding on the curriculum and facilitating yourself get you to engage (critically) with a lot with EA material. Especially for the former you have to think about the EA idea-space and work out a path through it all for fellows.

I helped create a fellowship curriculum (mostly a hybrid of two existing curricula iirc) before there were virtual programs or and this definitely got me more involved with EA. Of course, there may be a trade-off in quality. 

Some quick thoughts:

• EA Virtual Programs should be fine in my opinion, especially if you think you have more promising things to do than coordinating logistics for a program or facilitating cohorts
• The virtual Intro EA Program only has discussions in English and Spanish. If group members would much prefer to have discussions in Hungarian instead, it might be useful for you to find some Hungarian-speaking facilitators.
• Like Jaime commented, if you're delegating EA programs to EA Virtual Programs, it's best for you to have some contact with participants, especially particularly engaged ones, so that you can have one-on-one meetings exploring their key uncertainties, share with them relevant opportunities, encouraging them to  etc.
• It's rare for the EAIF to provide full-time funding for community building (see this comment)
• I'd try to see if you could do more publicity of EA Virtual Programs, such as at Hungarian universities

Your model here seemed to be that you should only run a fellowship program if you already have a strong community, but running a fellowship program is a way to build up a community. It has a strong track record with university groups. Admittedly, it is slightly less suited to the country context, but it can still work either remotely or by running groups in the most major cities.