I've never seen any studies showing that it does. It seems that most of the attention on ALA has been focused on its ability to induce translocation (moving to the cell surface) of the GLUT 4 transporter. This transporter moves glucose into the cell. Amino acids are shuttled into the cell by a seperate family of transporters.
It is plausible though that ALA could help transport amino acids by a general increase in insulin signalling. Insulin signalling is involved in amino acid transport. The first step in the insulin signalling cascade of events that ultimately leads to glucose and amino acid uptake is phosphorylation ( the addition of phosphate) of the insulin receptor. This activates the receptor, which in turn phosphorylates a number of other substrates, the best studied of which is IRS-1 (insulin receptor substrate 1).
R-ALA has been shown to do the same things: it induces phosphorylation of both the insulin receptor and IRS-1 (1). This could very well promote amino acid uptake as well as glucose uptake.
(1) Diabetologia 2000 Mar;43(3):294-303
Engagement of the insulin-sensitive pathway in the stimulation of glucose transport by alpha-lipoic acid in 3T3-L1 adipocytes.
Yaworsky K, Somwar R, Ramlal T, Tritschler HJ, Klip A.