Did Arjuna receive a curse from Urvashi to become as a eunuch?

Arjuna did not go to Heaven, as was narrated in the interpolated episodes in Vana Parva, ie., Arjuna’s fight with Shiva, Arjuna’s going to Heaven, etc.

Hence, his getting curse from Urvashi to become a eunuch is an interpolated story, which is as follows:

Arjuna was cursed by the Apsara Urvashi to become a eunuch because he rejected her romantic advances, addressing her as "mother" due to her past association with his ancestor Puru.

इयं पौरववंशस् जननी सुदतीति ह।

त्वामहं दृष्टवांस्तत्र विस्मयोत्फुल्ललोचनः ॥

न मामर्हसि कल्याणि अन्यथा ध्यात्रमप्सरः।

गुरोर्गरुतरा मे त्वं मम त्वं वंशवर्धिनी ॥

In the assembly I gazed at thee with eyes expanded in delight, thinking, 'Even this blooming lady is the mother of the Kaurava race.' O blessed Apsara, it behoveth thee not to entertain other feelings towards me, for thou art superior to my superiors, being the parent of my race.'"

——

When Yudhisthira queries Arjuna, at the verge of commencement of 1 year Ajnatavasa (अज्ञातवास), or "living in obscurity/to be lived incognito, as to how he would disguise himself in Matsya Desha of Virata, Arjuna replies as follows:

प्रतिज्ञां षण्ढकोऽस्मीति करिष्यामि महीपते । ज्याघातौ हि महान्तौ मे संवर्तुं नृप दुष्करौ ॥

कर्णयोः प्रतिमुच्याहं कुण्डले ज्वलनोपमे । वेणीकृतशिरा राजन्नाम्ना चैव बृहन्नडा ॥

पठन्नाख्यायिकां नाम स्त्रीभावेन पुनः पुनः । रमयिष्ये महीपालमन्यांश्चान्तःपुरे जनान् ॥

गीतं नृत्तं विचित्रं च वादित्रं विविधं तथा । शिक्षयिष्याम्यहं राजन्विराटभवने स्त्रियः ॥

प्रजानां समुदाचारं बहु कर्मकृतं वदन् । छादयिष्यामि कौन्तेय माययात्मानमात्मना ॥

युधिष्ठिरस्य गेहेऽस्मि द्रौपद्याः परिचारिका । उषितास्मीति वक्ष्यामि पृष्टो राज्ञा च भारत ॥

एतेन विधिना छन्नः कृतकेन यथा नलः । विहरिष्यामि राजेन्द्र विराटभवने सुखम् ॥

Arjuna replied, "O lord of the Earth, I will declare myself as one of the neuter sex. O monarch, it is, indeed difficult to hide the marks of the bowstring on my arms. I will, however, cover both my cicatrized arms with bangles. Wearing brilliant rings on my ears and conch-bangles on my wrists and causing a braid to hang down from my head, I shall, O king, appear as one of the third sex, Brihannala by name.

And living as a female I shall (always) entertain the king and the inmates of the inner apartments by reciting stories. And, O king, I shall also instruct the women of Virata's palace in singing and delightful modes of dancing and in musical instruments of diverse kinds. And I shall also recite the various excellent acts of men and thus conceal myself, O son of Kunti, by feigning disguise.

And, O Bharata should the king enquire, I will say that, I lived as a waiting maid of Draupadi in Yudhishthira's palace. And, O foremost of kings, concealing myself by this means, as fire is concealed by ashes, I shall pass my days agreeably in the palace of Virata."

——

If we study carefully the above saying of Arjuna, we can nowhere find him saying that he had received a curse from Urvashi and he would make use of it in the 13th year of exilement or 1 year Ajnatavasa (अज्ञातवास).

He had just disguised himself as neuter gender.