I don't know whether it's true or not, but it's definitely canonical. That is, the line does in fact appear in all the genuine versions of the Padma Purana. This includes the original Sanskrit version and the translations, though some of the translations try to get around mentioning it explicitly by using euphemisms. The Sanskrit word for 'testicle' is vṛṣaṇā, which appears as part of the word vṛṣaṇāvimau (Source). The translation that you found was definitely an accurate one.
Here's the full version of the one you're quoting, provided by Wisdom Lib:
For these goddesses give me food which is inaccessible in heaven, which is oily, mixed with jaggery, tasty and well-cooked and which is intended for them, and which is not enjoyed by anyone else before, O great god.
Thus addressed Maheśvara, the god of gods, told them in the vicinity of Pārvatī about their food:
“I have accomplished the food prepared in many ways. All that is exhausted. And no other (kind of food) is seen here.
Tell me what I should today give to you who have come (to me). I have especially to give something quite new.
126-127. I shall give you as food which has never been tasted before by anyone. Below my navel are these two circular long and fruit-like testicles. Even with this food you will have great satisfaction.
- Receiving that great favour all the goddesses saluted Śiva. Śarva said these words to them:
129-130. “The wealth, beasts, sons, wives and houses etc. of those who perform auspicious deeds without laughing, will be given to you by me; and also whatever else is in your mind. Those who by laughing have long teeth (i.e. show their teeth) (will) become poor.
- Therefore, one who is wise, should not indulge in censuring or laughing (at others). In this world you will be known as mothers.
132-133a. The lineage of those men, who, along with their relatives and kinsmen, prepare (articles from) a lotus, grams, and also cakes and sorts of bread with (i.e. having the shape of) testicles, as an offering, is not cut off.
133b-134. A man who has no son, gets a son; he, who desires wealth, obtains it; he, being handsome, lucky, enjoyer, well-versed in all sciences, is honoured in Brahmā’s world with (i.e. being taken in) a vehicle to which swans are yoked.
- O Śivadūtī, thus I have given them food. Does it bring shame to you?
I don't know what you mean by 'true,' but if your question is whether or not this story genuinely appears in the Padma Purana, the answer is: it does. This isn't a random story that somebody snuck in.
Nice question, though!