Yes, Upanishads often declares the same thing by four fruits for who attains the Brahman. 1. Amrutva 2. Moksha 3. BrahmaLoka 4. Liberation from joy and grief. (and 5. Ultimate Peace in some verse)
Actually Moksha means the ultimate liberation from birth-rebirth cycle in Samsara and Amrutva (immortality) is the state not bounded by time or space. So, they refers to the same. Jivatma experience joys and griefs, birth and re-birth in Samsara due to the Ajnana and Maya. And liberation from this bondage of Samsara is called Moksha. Who attains the Brahman, attains the Moksha and Amrutva.
Though there are numerous verses from Mukhya Upanishads to cite for those declaration, I'm currently citing from Katha Upanishad.
Liberation (retirement/renunciation) from joy and grief
तं दुर्दर्शं गूढमनुप्रविष्टं
गुहाहितं गह्वरेष्ठं पुराणम् ।
मत्वा धीरो हर्षशोकौ जहाति ॥ १२॥
1-II-12. The intelligent one, knowing through concentration of mind the Self that is hard to perceive, lodged in the innermost recess, located in intelligence, seated amidst misery, and ancient, abandons joy and grief.
अशरीरँ शरीरेष्वनवस्थेष्ववस्थितम् ।
महान्तं विभुमात्मानं मत्वा धीरो न शोचति ॥ २२॥
1-II-22. The intelligent one having known the Self to be bodiless in (all) bodies, to be firmly seated in things that are perishable, and to be great and all-pervading, does not grieve.
एतदालम्बनँ श्रेष्ठमेतदालम्बनं परम् ।
एतदालम्बनं ज्ञात्वा ब्रह्मलोके महीयते ॥ १७॥
1-II-17. This support is the best; this support is the supreme. Knowing this support one is magnified in the world of Brahman.
Moksha (Liberation from Samsara):
यस्तु विज्ञानवान्भवति समनस्कः सदा शुचिः ।
स तु तत्पदमाप्नोति यस्माद्भूयो न जायते ॥ ८॥
1-III-8. But whoso is possessed of a discriminating intellect and a restrained mind, and is ever pure, attains that goal from which he is not born again.
तथाऽरसं नित्यमगन्धवच्च यत् ।
अनाद्यनन्तं महतः परं ध्रुवं
निचाय्य तन्मृत्युमुखात् प्रमुच्यते ॥ १५॥
1-III-15. By knowing that which is soundless, touchless, formless, un-decaying, so also tasteless, eternal, odourless, beginningless, endless, subtler than Mahat and constant, man is liberated from the jaws of death.
य एष सुप्तेषु जागर्ति कामं कामं पुरुषो निर्मिमाणः ।
तदेव शुक्रं तद्ब्रह्म तदेवामृतमुच्यते ।
तस्मिँल्लोकाः श्रिताः सर्वे तदु नात्येति कश्चन । एतद्वै तत् ॥ ८॥
2-II-8. This Purusha who is awake when all are asleep, creating all things cherished, is certainly pure; that is Brahman; that is called the Immortal. All worlds are strung on that; none passes beyond that. This verily is that (thou seekest).
Note that Upanishadic Amrutva (immortality) is not the body related immortality which we usually find obtained as a boon neither what is experienced in SwargaLoka.
You can also see the beauty of Upanishads when they declares these fruits combined!
2-II-1. The city of the unborn whose knowledge is like the light of the sun, consists of eleven gates. Meditating on Him, one does not grieve and, becoming free (from bondage), one becomes liberated. This verily is that (thou seekest).
2-III-8. But subtler than Avyakta is Purusha, all-pervading and without a linga (distinguishing mark) indeed, knowing whom a mortal becomes freed and attains immortality.