If the disk controller does not use compression, then Synetech's answer is correct and encryption will not change anything. If the controller uses compression then encryption will probably reduce the lifespan of the disk (compared to an identical disk where encryption is not used).
Some SSD controllers use compression in order to minimize the amount of data written to the actual flash chips and in order to improve read performance (SandForce controllers are a prime example, there may be others). This will work best if the data written to the disk is easily compressible. Text files, executables, uncompressed images (BMP for example) and similar can usually be compressed quite a lot while files that are already compressed or are encrypted are almost impossible to compress since the data will look almost completely random to the compression algorithm in the controller.
Tom's Hardware made a nice test about precisely this on an Intel SSD 520 which can be found at
What they basically do is measure the write amplification (the ratio of the amount of data written to flash and the amount of data sent to the drive) of the drive when writing completely compressible data and completely random data. For completely random data, the write amplification is 2.9* which means that for every GB of data sent to the disk, 2.9 GB are written to flash. The article notes that this seems to be roughly the same number measured on drives that do not use compression. For completely compressible data, the ratio is 0.17 which is quite a bit lower.
Normal usage will probably end up somewhere in between unless the data is encrypted. The lifetime predictions in the article are somewhat academic, but shows that encryption could definitely affect lifetime on an SSD with a SandForce controller. The only way to get around this would be if the controller itself can do the encryption after compression has occurred.
*The article does not specify why 2.9 is considered a normal value and I have not really researched it. A logical explanation could be that most SSDs use MLC NAND which is a bit error prone (bit flips in other parts of erase blocks can occur while writing if I recall correctly). In order to correct for this, data is probably written to several places so that recovery or correction is always possible.