Sometimes. If you try to enter country A from country B showing a passport of country C, country A could find out that you also hold a passport of country D in any of the following cases:

1. You volunteer the information. (Immigration officers sometimes ask if you have ever been a citizen or used a passport of a different country. If you are asked, you may or may not have a right to remain silent, depending on your citizenship and what country you are trying to enter. refusing to answer is likely to be treated as suspicious, at best, and may -- again depending on the country and your citizenship -- lead to denial of entry or intensive search .)
2. You show the passport of country D, they spot it, or they find it during a search. (You can't rule this out if you have the other passport with you, since a "random" but thorough search is always a possibility.)
3. Information about your passport of country D is included in PNR or API data sent by the airline to the government of country A, or accessed by that government from the CRS that hosts the airline's reservations.
4. Country A already has both passports linked in their database about you (This is most likely if one of the above things has happened on a previous entry or exit, or if some other unique or unusual identifier, such as a name and date of birth, phone number, etc. has enabled them to link the records of entries and exits with the different passports.)

The AIRIMP formats used to transmit passport info don't require a unique passport number per passenger, but some CRS's *may* have inhibited entry of multiple passport numbers in the PNR for a single passenger. Most airlines and travel agencies don't directly disclose what data is entered in PNR's, so the only way to find out is to ask.

In the USA, the formats for API data are SSI, and passengers have no right to see their PNR. Passengers making reservations in Canada or the EU, with Canadian or EU airlines, or with airline offices or online or offline travel agencies in Canada or the EU are entitled to request their PNR and API data.

In reviewing the (late, incomplete, improperly redacted) responses of airlines and the CBP to requests for PNR and API data, I have never seen more than one passport for the same passenger in a single API record. From travel agency experience, I know that multiple passports sometimes up in the same PNR, although not necessarily in standardized format.

I suspect that the most likely way for country A to realize that you have both passports C and D would be if they have been entered in PNR's or API records for different trips, but those PNR's or API recrods have been correlated into your "Automated Targeting System" and/or TECS record in the USA, or a similar "travel history" with another country. I have seen ATS and TECS records, including my own, with different passport numbers for different trips (because of renewed or replaced passports with new numbers). I haven't seen one with passports form different countries, but I assume that it is possible.

The way to find out what's in your records is to ask for them.