Using only the site search engine will be sufficient in many cases, for many surnames, orphanage names, etc., but not in all cases. [This would be true of any search engine and not just the one currently in use here.] You will also need to search the individual transcriptions:
Portions of the censuses can be very hard to read, some segments can't be read at all. Sometimes only one or two letters of a surname can be discerned; in other cases, surnames are readable except for one or two letters. In such cases the transcriber will record the surname as "????en????" or "R?????" or "D???g???" (depending on what the surname is and what portion of that surname was readable to that transcriber). Unless you know exactly what portion of the name was discernible by the transcriber and the exact number of question marks used by the same transcriber to represent your ancestor's name, the hits you receive back from the site search engine may or may not be very helpful to you** (please see the example below). With regard to searching by "orphanage name": sometimes the Enumerator did not record the full name of the orphanage in the census which means, in turn, that the transcriber can not include the name of that orphanage as part of the transcription. As a result, an effective search must also include examination of the actual transcriptions.
I am in the process of working out a more focused surname search index (which will include the illegible surnames & involve one more round of proofreading per list) for researchers to use in addition to the site search engine, but this will take some time to complete and put in place. In the meantime, please keep in mind your need to search the individual transcriptions as well. If your computer can not handle some of the larger web pages, please let me know.
**EXAMPLE: Your orphan's surname was 'Dentison' and family lore places him in an orphanage in New York --- named either "Children's XXXXX" or "XXXXX Children's (Home)" ...