(Originally a Facebook comment. More detail here.)
If you suspect that something in your family indicates Crypto-Jewish heritage, it definitely could. My father’s family often did similarly when they became or had been Crypto Jews—if they, e.g., could avoid the predominant denomination (Russian Orthodox in Poland) and even put off any rites, they did. For example, one matriarch (“Katarzyna” Danilowicz Czerniecki) was not forcibly baptized until she was five, and one patriarch (Mihály Trudnyak né Nagy) in Hungary was “illegitmate” because his parents refused to marry in a Roman Catholic church—both of his siblings (Zsuzana and Mária) were “illegitimate” as well, and they lived in a different house when each sibling was born. They wanted to avoid an Austrohungarian inquisition.
They also denomination switched like it didn’t matter to them when they did because it didn’t matter to them—one, as I recall, Morgiewicz or Margiewicz even became a Congregationalist! It held no religious significance for them (and if you think that I’m going to be able to link to every record at every moment, you’re—to put it politely—being meshugah on purpose. I have other things to do, including to manage my ADD and Generalized Anxiety Disorder, as well as to help fellow Jew avoid equivalents of inquisitions by other fellow Jews. Anyway, about the denomination switching…)
Even if it had a religious significance, the ethnic Jewishness was kept in the family—unless gentile cousins spoke about it when they weren’t supposed to do so (which two Shackel/Staskiel cousins of one of my Andrulewicz cousins did, and a note about him being a “JEW” was made in the payroll sections of his employment cards twice. One card reads “44-JEW” and “44-JEW-1”).
It also came out in small hints left by family—e.g., to this day, I don’t think that many family members appreciate that my great-grandaunt Helen Rusnak Ropel left the wonderful gift of giving her father‘s Hebrew name when she died. As it clicked when I realized what she left for the burial records to hold, my paternal grandmother’s maternal grandfather used “Stef” or “Stephen” (or variants thereof) to calque for “Yosef”. I thought that there was a mistake at first. Then I realized how brave Great-Grandaunt Helen was. Even though she couldn’t give it in life, she was going to make sure that she could give her fathers name as ”Joseph Rusnak” before she left this life.
(By the way, on the secular calendar, she died on my 18th birthday. I was able to confirm that I’m Jewish on another side in the July of that year.).
Be prepared, by the way, to have family treat you horribly over finding out that you’re Jewish.  I actually, e.g., fell out with one maternal cousin because he or she was not happy that I found out that we are mixed-blooded Jews on one particular side (i.e., Lehr-Pundt, and I will give no more hints as to what cousin. I have multiple cousins on that side across generations, and I don’t want to dox anybody or give any other attention—whether positive or negative—to anyone whom hates me that much. If he or she happens to read this—and he or she knows who he or she is—he or she can deal with the fact that I was able to confirm with a Lehr cousin that we are Jewish. Of course, ironically, that cousin of mine fell out with me over political differences—and differences which are not good for the Jewish people as a whole, might I add).