If one donates tzedaka online for a yeshiva or kollel, are we fulfilling the mitvah of tzedaka?
The question arises since in all probability none of that money will actually reach the hands of those who are really sitting and learning, (who only receive a relatively small fixed amount each month anyway, which is by far, not even remotely sufficient to live on and support a family), rather it all goes directly to the heads of the institution, the administration, and the various office employees, as well as to pay the various upkeep expenses.
It would seem the best strategy is to find someone sitting and learning and give them personally a direct donation in order to be certain to properly fulfill the mitzvah of supporting those who learn Torah.
A person can definitely fulfill the mitzva of tzedakah by donating to a kollel or yeshiva online. Supporting those talmidei chachamim that are learning torah, does not apply exclusively to paying their grocery bills. Paying for the electricity of the yeshiva so that the beis midrash has lights and air conditioning is also support the actual learning, and so is paying for the furniture in the bais midrash. In fact even paying the salary of the staff of the Yeshiva, is also supporting torah, as without them having a way to live they would not be able to teach the students. Why is paying the rent of the apartment of the kollel person more tzedakah than paying the rent of the beis midrash?! They are both supporting and helping the person to be able to sit and learn.
If you personally feel that it is bigger mitzva to give cash straight to the kollel person, by all means you may do so. Different people have various preferences of who and what they want to spend their maaser money. However, in the eyes of Hashem it doesn’t seem that one way of supporting torah is different than the other.
As a side point, there is a preference to giving tzedakah in a way that you don’t know who the por person is and the poor person doesn’t know who you are. By donating online, you would have this preference, over giving the money directly to the poor person.
שולחן ערוך יורה דעה הלכות צדקה סימן רמט סעיף ז
פחות מזה, הנותן צדקה לעני ולא ידע למי יתן, ולא ידע העני ממי מקבל. וקרוב לזה, הנותן לקופה של צדקה; ולא יתן אדם לקופה של צדקה אלא אם כן יודע שהממונה עליה נאמן ויודע לנהוג בה כשורה.