My intuition tells me this would absolutely limit growth. Trade and all types of borrowing including personal loans, mortgages, and interest rates on credit cards would be seriously limited.
From the standard monetary equation, the only way to raise the standard of living would be through deflation (a decrease of the average price of goods during the year).
Economy could continue on working. Prices would eventually adjust. As you mentioned in your question this would lead to perpetual deflation.
That would make unemployment unnecessarily high during depression but there is no conventional growth theory that would require extra money supply.
Economic growth (in per capita terms) is dependent on technological growth, savings rate, investments in human capital and potentially some other factors like technology spillovers from trade or learning by doing (see Acemoglu Introduction to Modern Economic Growth 2nd edition).
