Are there any effects of elevated Cysteine levels on cognitive function?
Your shown homocysteine pathway is way too simple. Especially the production of the neuromodulator H2S from excess sulfur amino acids is not shown. In the last years many more enzymes and reactions have been discovered. I have summarized human sulfur amino acid metabolism in reactome.org, so please use this link to discover all the details and new papers. I'll also append some of the relevant papers below.

Brosnan, JT, Brosnan, ME The sulfur-containing amino acids: an overview 2006 J Nutr PMID 16702333

Remethylation of homocysteine to methionine can also happen using betaine as a methyl donor. This reaction is also part of choline catabolism.

Li, F, Feng, Q, Lee, C, Wang, S, Pelleymounter, LL, Moon, I, Eckloff, BW, Wieben, ED, Schaid, DJ, Yee, V, Weinshilboum, RM Human betaine-homocysteine methyltransferase (BHMT) and BHMT2: common gene sequence variation and functional characterization 2008 Mol Genet Metab PMID 18457970

Bearden, SE, Beard RS, Jr, Pfau, JC Extracellular transsulfuration generates hydrogen sulfide from homocysteine and protects endothelium from redox stress 2010 Am J Physiol Heart Circ Physiol PMID 20817827

Dominy, JE, Stipanuk, MH New roles for cysteine and transsulfuration enzymes: production of H2S, a neuromodulator and smooth muscle relaxant 2004 Nutr Rev PMID 15497768

Stipanuk, MH, Ueki, I Dealing with methionine/homocysteine sulfur: cysteine metabolism to taurine and inorganic sulfur 2011 J Inherit Metab Dis PMID 20162368

Chiku, T, Padovani, D, Zhu, W, Singh, S, Vitvitsky, V, Banerjee, R H2S biogenesis by human cystathionine gamma-lyase leads to the novel sulfur metabolites lanthionine and homolanthionine and is responsive to the grade of hyperhomocysteinemia 2009 J Biol Chem PMID 19261609