The answer (maybe)¹ is no. In the following paper,

Gabriel Robins and Jeffrey S. Salowe, On the maximum degree of minimum spanning trees. Proceedings of the tenth annual symposium on Computational Geometry (SCG '94), 250-258 (1994). PDF.

The authors prove that under the $L_p$ norm, the maximum vertex degree over all MSTs is equal to the kissing number of the corresponding unit ball;

¹ I said 'maybe', since I have not checked the proof of the mentioned paper.

The answer (maybe)¹ is no. In the following paper,

Gabriel Robins and Jeffrey S. Salowe, On the maximum degree of minimum spanning trees. Proceedings of the tenth annual symposium on Computational Geometry (SCG '94), 250-258 (1994). PDF.

The authors proved that under the $L_p$ norm, the maximum vertex degree over all MSTs is equal to the kissing number of the corresponding unit ball;

¹ I said 'maybe', since I have not checked the proof of the mentioned paper.

The answer (maybe) is no. In the following paper,

Gabriel Robins and Jeffrey S. Salowe, On the maximum degree of minimum spanning trees. Proceedings of the tenth annual symposium on Computational Geometry (SCG '94), 250-258 (1994). PDF.

The authors prove that under the $L_p$ norm, the maximum vertex degree over all MSTs is equal to the kissing number of the corresponding unit ball;

The answer (maybe)¹ is no. In the following paper,

Gabriel Robins and Jeffrey S. Salowe, On the maximum degree of minimum spanning trees. Proceedings of the tenth annual symposium on Computational Geometry (SCG '94), 250-258 (1994). PDF.

The authors prove that under the $L_p$ norm, the maximum vertex degree over all MSTs is equal to the kissing number of the corresponding unit ball;

¹ I said 'maybe', since I have not checked the proof of the mentioned paper.