The short answer is no, not anywhere close to 200ppm and not appreciably lower than ambient conditions. The modern standard for buildings is a full air change every three hours. This means your houseplants would need to achieve your target level on a full house volume of air every three hours. There is no practical arrangement which will achieve this.
The long answer is ...
The photosynthesis equation is 6CO2 + 6H2O ------> C6H12O6 + 6O2.
Corn one of the most efficient photosynthetic producers of calories. It can produce 15 million kilocalories per acre under good conditions. That's 1.5 * 1010 calories.
Let's say you have a 5x5x3m house.
You have floorspace for 25m2 of field corn (you will just have to fit yourself in somehow). An acre is 4,046 m2 so 25m2 is 25 / 4046 of an acre, or 0.6%. So you can produce 6 * 10-3 * 1.5 * 1010 calories in this setting. That's 9 * 107 calories. Let's say you take really good care of the corn and manage 1 * 108 calories.
A gram of glucose provides 4 * 103 calories of energy when used. So the amount of glucose that contains 108 calories is (108 calories / 4 * 103 calories), or 2.5 * 105 grams.
The molar mass of glucose is 1.80 * 102 g mol-1. Therefore there are 1 g / 1.80 * 102 g mol-1 gives the number of glucose molecules in a gram - around 5 * 10-3 mols or 3.3 * 1021 molecules.
2.5 * 105 grams of glucose is therefore 3.3 * 1021 molecules/gram * 2.5 * 105 grams = 8.2 * 1026 molecules of glucose.
Each molecule of glucose requires 6 molecules of CO2 to create. 8.2 * 1026 molecules of glucose times 6 is around 5 * 1027 molecules of CO2. This is how many molecules of CO2 will be removed from the air by the corn in your house over the course of a growing season.
It takes a growing season to use this much CO2. There are around 102 days in a growing season. So each day your corn will take 5 * 1025 molecules of CO2 out of the air for you.
A human breaths out about 40000ppm CO2 which comes to about 1.27 * 103 grams of CO2 per day. Given the molar weight of CO2, this is around 1.27 * 103 g / 1.17 * 102 g mol-1 or 1 * 101 moles of CO2, or 6 * 1023 molecules of CO2.
You have an air volume of 75m3. At a concentration of 440ppm, under somewhat normal conditions, there are about 2.5 * 1025 * (440/1000000) molecules of CO2 in a m3 of air, or around 1022 molecules. So in your house you have 7.5 * 1023 molecules of CO2. If you use about half of these you'll reduce the concentration to 200ppm.
So to bring the concentration of CO2 in the house from 440ppm to 200ppm with 75m2 of corn growing and 1 human breathing will take:
(amount CO2 to remove) / ((rate of removal) - (rate of addition))
(1.25 * 1025 molecules CO2) / ((5 * 1025 molecules CO2 / day) - (6 * 1023 molecules of CO2))
The human contribution ends up being pretty negligible (around 1% of the corn contribution) so we can drop it.
(1.25 * 1025 molecules CO2) / (5 * 1025 molecules CO2 / day)
or 0.25 days, or 6 hours.
This is about half the rate you need to achieve a steady state of 200ppm in the house. I've also assumed rate of use of CO2 due to photosynthesis does not fall as CO2 concentration falls (which it probably does).
Given that it's not very likely anyone wants to live in what amounts to an indoor corn field, any practical use of houseplants to alter CO2 is likely to have negligible effects.
Given the rates figured here, you can decide how much of your household you are willing to devote to corn, determine the reduced rate, and figure out what the equilibrium CO2 level will come to (very roughly, of course). You may also want to adjust for other CO2 sources such as higher or lower inside/outside air exchange rate (for a leaky house or a poorly built office, respectively), combustion products (cooking, etc).