Well depends. A lot happened in that time.

First of all Moravia mostly stayed Catholic. So even Catholic Moravians fled to Bohemia.

The Hussite wars didn't start until 1419. So before that, no.

During the Hussite wars many did join the Bohemican cause, but more Catholics fled than Protestants came.

After the wars some did come, but not from far and wide.

After Martin Luther starting in 1517 Northern Germany underwent similar rebellions. During this time the Hapsburgs tried to keep the Lutheran militants from influencing Bohemia.. so it wasn't exactly safe in Bohemia either.

When the dust settled is where it gets interesting.

Toward the end of the 16th century, your answer is "Yes". Under Rudolf II many came to Prague because protestants were relatively not discriminated against under his reign.

Johannes Kepler is one such example. A lutheran that had issues Southern Germany, and also to some degree in Austrian Graz, but was fine in Prague. The first public autopsy was done by Jan Jessenius in Prague. Tycho Brahe (protestant from Denmark) was welcome in Prague. Edward Kelley and John Dee, (technically protestants, at least Kelley, Dee really wasn't at all a Protestant) went to Bohemia when the heat got to hot in London (for alchemy, not religious persecution.. but Dee was seen as a "conjuror", which Rudolf II couldn't get enough of)

So your answer is No until 1419 then yes during the Hussite Wars. Then basically yes until Luther, then still kinda yes despite the Hapsburgs. Then No. Then Yes after Rudolf II (in the 1580's). And a strong NO until the 30 years War (which is after the timeframe you asked) and Protestants fled Bohemia until the end of the war (and after the war the population was protestant, but the Catholic Austrians ruled with an iron fist until it started to let up at the the end of the 19th century a bit - until Independence.. by then the issue of Catholic/Protestant was long resolved. Czechs had had enough of religion by then, and today are the most atheistic country in the world by some measures.)

Anabaptists are not always accounted "Protestants" in Reformation historiography. If you'll allow the general "not Catholic" definition, however:

Moravia was probably the closest thing early Anabaptists (1520s-1620ish) had to a refuge, although things did not always work out so well. Significant populations of Anabaptists fleeing worse persecution in southern Germany, Switzerland, and Tirol ended up in Moravia, along with major leaders like Hubmaier, Hut, and Hutter.

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The 1485 Peace of Kutna Hora was an agreement between Catholic and Utraquist (the more conservative branch of the Hussite Church) nobles to allow the coexistence of both forms of religious practice in Moravia. Although the agreement did not officially apply to the more radical Hussite branches, in practice many nobles extended the leniency to the (Hussite) Brethren in the early 16th century. This attitude and experience of toleration so long as there was no political threat likely contributed to early tolerance towards Anabaptists in the second half of the 1520s--they are sometimes accounted "German Brethren" in sources, reflecting their foreign origin as refugees.

Well, in areas controlled by Moravian nobles rather than the emperor. For example, Hubmaier was arrested and executed when the town he reformed (Nikolsburg) reverted to imperial control.

The Anabaptist community in Austerlitz in particular attracted a decent amount of refugees from abroad. Eventually it split, with one group following Jakob Hutter to Auspitz. The Hutterites do get exiled from Auspitz, but manage to be the only recorded group of Moravian Anabaptists to survive, as a group, the major persecutions of 1535. Yes, these are the original Hutterites who are still around today. There are also some diffuse reports of Anabaptists and very small groups of Sabbatarians, a sect that grew out of Nikolsburg Anabaptism after Hubmaier's execution.

Following the empire's suppression of the Bohemian Revolt and their seizure of the nobility's lands, Anabaptism was outlawed in 1620. The Hutterites fled to Hungary in 1622.

If you're interested: Martin Rothkegel provides a very nice overview of Anabaptism in Moravia (as well as its minor presence in Bohemia and Silesia), with excellent footnotes to the secondary scholarship and some primary sources, in A Companion to Anabaptism and Spiritualism, 1521-1700, ed. Roth and Stayer.