The short answer is Yes.

Here are some of the details. You start with a crystal for the representation. You don't need to specify which model you are taking. When you take a tensor product a subset of the vertices of the crystal give highest weight vectors. The rule is a simple rule depending on the depth (or rise) of the vertex.

For the fundamental representation this is particularly straightforward.

The short answer is Yes.

Here are some of the details. You start with a crystal for the representation. You don't need to specify which model you are taking. When you take a tensor product a subset of the vertices of the crystal give highest weight vectors. The rule is a simple rule depending on the depth (or rise) of the vertex.

For the fundamental representation this is particularly straightforward.

If you want to get started with crystals, a good place to begin is:

MR1881971 (2002m:17012) Hong, Jin ; Kang, Seok-Jin . Introduction to quantum groups and crystal bases. Graduate Studies in Mathematics, 42. American Mathematical Society, Providence, RI, 2002. xviii+307 pp. ISBN: 0-8218-2874-6

This does not discuss the tensor product rule you asked for. The original reference for for the general tensor product rule is:

MR0225936 (37 #1526) Parthasarathy, K. R. ; Ranga Rao, R. ; Varadarajan, V. S. Representations of complex semi-simple Lie groups and Lie algebras. Ann. of Math. (2) 85 1967 383--429.

This tensor product rule requires further notation. The advantage is that multiplicities are calculated directly without any cancelation.