The question is somewhat difficult to answer, because the reactions to HRT are very individual. They depend on things like your age, your genetic make-up and the kind of HRT you get (what kind of drugs, what dosage, etc.)
To put things as general as possible: If you start HRT you may first feel euphoria, which is (more often than not) a purely psychological reaction. The actual effects of HRT will usually begin to manifest after a few weeks (once again: highly depending on what you are taking and how your body reacts to it). Unlike the initial psychological effect this will usually be more gradual, as your body and mind "ease into" their new state of being.
The obvious physical effects usually take months to manifest (growth of breast tissue, etc), though infertility can come earlier, particularly if you take anti-androgens or progesterone.
Because you specifically asked about sperm, the effects of HRT are (mostly) reversible in that regard, particularly if you haven't taken HRT for long. Some people can become fertile after months, sometimes even years of HRT, once they stop taking it.
So: Yes, most people can stop HRT for a while, freeze some sperm and then go back on. There are no guarantees, but it works far more often than not.
Of course. ヾ(＾▽＾)ﾉ