Yes. If you do a normal format, the old data can be recovered. A normal format only deletes/overwrites a tiny bit of filesystem metadata, but does not overwrite all of the data itself. The data is still there. This is especially true on SSDs, due to wear levelling and other features of SSDs.
The following research paper studies erasure of data on SSDs:
One takeaway lesson is that securely erasing data on a SSD is a bit tricky. One reason is that overwriting data on a SSD doesn't work the way you'd think it does, due to wear-leveling and other features. When you ask the SSD to "overwrite" an existing sector, it doesn't actually overwrite or delete the existing data immediately. Instead, it writes the new data somewhere else and just change a pointer to point to the new version (leaving the old version laying around). The old version may eventually get erased, or it may not. As a result, even data you think you have erased, may still be present and accessible on the SSD.
Also, SSDs are a bit tricky to sanitize (erase completely), because the methods that used to work for magnetic HDDs don't necessarily work reliably on SSDs (due to the aforementioned wear levelling and other issues). Consequently, utilities that are advertised as providing "secure drive erase" functionality may not be fully secure, if applied to a SSD. For instance, the FAST paper found that, in most cases, performing a full overwrite of all of the data on the SSD twice was enough to sanitize the disk drive, but there were a few exceptional cases where some of the data still remained present. There may be other reasons not to want to perform repeated overwrites of the full drive: it is very slow, and it may reduce the subsequent lifetime of the drive.
The FAST paper also found that degaussing (a standard method used for sanitizing magnetic hard drives) is not effective at all at sanitizing SSDs.
Moreover, the FAST paper found that standard utilities for sanitizing individual files were highly unreliable on SSDs: often a large fraction of the data remained present somewhere on the drive. Therefore, you should assume there is no reliable way to securely erase individual files on a SSD; you need to sanitize the whole drive, as an entire unit.
The most reliable way to securely erase an entire SSD is to use the ATA Secure Erase command. However, this is not foolproof. The FAST paper found that most SSDs implement this correctly, but not all. In particular, 8 of the 12 SSDs they studied supported ATA Secure Erase, and 4 did not. Of the 8 that did support it, 3 had a buggy implementation. 1 buggy implementation was really bad: it reported success, but actually left the data laying around. This is atrociously bad, because there is no way that software could detect the failure to erase. 2 buggy implementations failed and left old data laying around (under certain conditions), but at least they reported failure, so if the software that sends the ATA Secure Erase command checks the result code, at least the failure could be detected.
The other possible approach is to use full disk encryption: make sure the entire filesystem on the drive is encrypted from the start (e.g., Bitlocker, Truecrypt). When you want to sanitize the drive, forget all the crypto keys and securely erase them, and then erase the drive as best as possible. This may be a workable solution, though personally I would probably want to combine it with ATA Secure Erase, too, for best security.
See also the following questions on this site: