Britta Glennon reports in an NBER working paper that the two go together.

Skilled immigration restrictions may have secondary consequences that have been largely overlooked in the immigration debate: multinational firms faced with visa constraints have an offshoring option, namely, hiring the labor they need at their foreign affiliates. If multinationals use this option, then restrictive migration policies are unlikely to have the desired effects of increasing employment of natives, but rather have the effect of offshoring jobs. Combining visa data and comprehensive data on US multinational firm activity, I find that restrictions on H-1B immigration caused foreign affiliate employment increases at the intensive and extensive margins, particularly in Canada, India, and China.