From what I searched and found Lord Ganapati/Ganesha was also practised in all 4 schools including Gelugpa. He is mainly propitiated to assist in resources or wealth. But I haven't found a source that Lama Tsongkhapa did his practise. But definitely it is not uncommon in Tibetan Buddhism. Some info I have found regarding Lord Ganapati below...
Hope someone could give more info on whether Lama Tsongkhapa did any of his practise.
The Buddhist Ganapati is also known in classical Indo-Chinese-Japanese tantra of the Shingon school. This means Buddhist Ganapati travelled to Japan SEPARATELY from the central Asian Nepalese Tibetan connection. Thus it is guaranteed to have been practiced by Buddhists in ancient India before the development of "Tibetan Buddhism", and independently of "Tibetan Buddhism".
Tantric Buddhist Ganapati in the Sakya School is, according to the rite of initiation, a sub-manifestation of Amitabha Buddha as Avalokitesvara ( "Chenresig" ). He is Twelve Armed and crowned by Amitabha Buddha. This may not be true of the Japanese Shingon school of tantra.
Source:
http://tibetanbuddhism.tribe.net/thread/50e889bd-6853-4bc8-8904-6d090201fafaGanesha and TibetGanesha Scriptures were translated into Tibetan and introduced in Tibet by the monks by 10 and 11 c. Though based on Indian Scriptures Ganesha acquires a very different form outside India. For Tibetan and Tantric Buddhists, Ganapati is the Sanskrit name commonly used and the word found in Tibetan literature too. The two words Ganesha and Ganapati have the same basic meaning in English: lord of Ganas.
In one Tibetan form he is shown being trodden under foot by Mah?kala, who is a Dharmapala (“protector of dharma”) in Vajrayana Buddhism (Tibetan Buddhism and Japanese Shingon Buddhism). Mahakala (Shadbhuja) in the six-armed form is also an emanation of Avalokiteshvara. In this form he stands atop an elephant headed supine figure. The name of the figure varies from ritual text to ritual text but is commonly referred to as Vinayaka. As the Buddhist god Vin?yaka, he is often shown dancing, a form called Nritya Ganapati
Source:
http://theemerald.wordpress.com/2009/03/19/buddhist-deity-ganapati/